I have used Synaptic Package Manager to install version 1.0-0 cafugeo of b43-firmware on my Inspiron 1525 running Ubuntu. The purpose is to make my system connect to my wireless router. The system still does not seem to use the firmware (I assume this is the driver) to see the router. Your guidance, please.
Supplementary question: Do I need to install b43-fwcutter too, please?

Yes, you need to install the fwcutter and the proper b43 driver. Check out http://wireless.kernel.org/en/users/Drivers/b43 for more information.

Thank you for your fast response. I read the link but I am not confident of following the instructions. I'll need some time to experiment.

I'm going to potentially disagree with Zyglow's advice. You've got two things you need to deal with here:

1) The b43 driver - This is part of the kernel and was almost certainly installed as part of Ubuntu
2) The b43 firmware - This was almost certainly NOT installed with Ubuntu (Broadcom's license doesn't allow it) and this is where things might get a bit tricky. The fwcutter program has one purpose only, and that is to create the b43 firmware files. If the Ubuntu package you installed takes care of this, then you don't need fwcutter.

So what you need to do is three things:

1) Open a console and (as root) run lsmod. That will show you all of the loaded kernel modules, and b43 should be there
2) Look in /lib/firmware and see if there are any firmware files there that look like they are for b43
3) Look in your log files (/var/log/syslog, /var/log/messages and the output of the dmesg command) and see if b43 is leaving any clues as to what is going on.

Thank you, Hangdog42, and especially for spelling out the commands; Linux commands are foreign to me. When I followed your instructions step by step, I found results that seem contrary to your expectations, thus:
1)The *lsmod* command run in the terminal application showed no b43.
2)*ls /lib/firmware* gave 2.6.24-16-generic 2.6.24-18-gneric b43 b43legacy. That seems to say the b43 firmware has been installed though not necessarily with Ubuntu, since, so I think, that using Synpatic Package Manager, I had installed b3-firmware of 1.0-0cafuego before I started this question thread.
3)Both *ls /var/log/syslog* and *ls /var/log/messages* returned nothing but /var/log/syslog and /var/log/messages respectively. *dmes* showed no trace of b43, nor other information (to my layman eyes) that is related to b43.

Your further guidance will be greatly appreciated.

Hm. OK, you'll have to humor me a bit here, but we need to identify what chipset your card is running. If you don't happen to know this, try running lspci in a console and see if your wireless card is listed. Most Dell wireless cards are some form of Broadcom chipset, but we need to see which one. The reasons this is important is that there are actually two versions of the b43 driver, b43 itself and b43-legacy which is needed for some older Broadcom chipsets.

I agree with you here. Unless there is later evidence that the firmware is a problem, we can probably assume that it has been installed and we don't need to worry about using fwcutter.

If you want to see if just loading the driver works, in the console run modprobe b43 and see if that brings your wireless card to life. You will definitely have to be root to do this. If modprobe works, it just returns you to the command line prompt without saying anything, however then b43 should appear in the lsmod output and you'll likely see stuff in your log files. If modprobe fails for some reason, it will tell you why, in which case, post the output.

Check if you have build-essential package,if not,open the terminal and run this
Then do this;
Then download the Broadcom firmware and install it.After that do this;
"FIRMWARE_INSTALL_DIR" must point to the directory where your firmware directory is.
Reboot.

Lspci run. The chipset is BCM4310.
It took me quite an effort to figure out how to get to be root. modprobe b43 run and it returned me the command prompt without saying anything. Yes b43 appeared in the lsmod output. Then I knew not what next to do.
Later I thought perhaps I should load bcm43xx-firmware with Synaptic Package, and I did, apparently not solving the problem.
I also followed alan_ri's suggestion as described in my next reply going to him. Please see that reply too.
During my attempt to escape from the BCM maze, I tried Internet connection by wireless from time to time, hoping that I would stumble into success, with no luck.
Thank you for your patience, Hangdog42.

I followed Hangdog42's second guidance message without success, but my reply to him may help you figure out where I made mistakes.
As you suggested, I checked the presence of build-essential with Synaptic Package Manager, which showed I don't have build-essential installed. Preparing to install it (but I used Synaptic Package Manager for ease of use), I noticed the following description: If you do not plan to build Debian packages, you don't need this message. (etc.).
I looked up what Debian package was and could not decide that I needed it. I felt I should check with you first. Hence this reply.
Many thanks, Alan_ri.

build-essential package is not going to do any harm to you or your computer,it's just a package that will make it possible for you to build .deb packages on your computer,to clarify,it's something like a program in Windows that builds files with .exe extension,so please just follow the guide from my post and you should be fine.
Here is a link where you can read about Ubuntu package managment system and here's a link for sudo manual.

If b43 appears in the lsmod output, then your wireless card should be available for use. The only thing that would prevent it from functioning is if the firmware isn't right. So there are a couple things to do

1) Look in either the output if iwconfig or in whatever GUI monstrosity Ubuntu uses after b43 is loaded and see if you have a wireless card avaialable. If so, you can configure it with your SSID and any encryption information and hopefully that will allow you to get an IP address.

2)If you don't seem to have a functioning wireless card after loading b43, then you need to look in your log files (/var/log/syslog, /var/log/messages, and the output of dmesg) and see if b43 is complaining about anything.

After hours of trying out over two days your suggestions, branching out to configurating the network, restarting to make sure changes take effect, plugging in and unplugging the ethernet wire and doing all sorts of other things that seemed remotely related, I still cannot make the wireless connection work. The worse thing is that I have even lost connection by wire! and nothing doing can revive it. I am writing this post with my wife's Windows system. What a shame.
Clearly I am technically inadequate to use Ubuntu Linux, even though I like the features of Linux and the applications in the distribution. I am sure installing other application software, such as Limewire, would be breeze if I can only make the wireless connection work.
The bottom line is, I think I'll have to get phone help. I looked at Canonical's price; it's $250 for a year. It would be too expensive for me, plus I hope I don't need help for a year. Are much less expensive alternatives with some other companies, please?

This is the wrong conclusion to be drawing from your experience. The problem you're facing is that Broadcom refuses to support Linux in any way, so the drivers have been reverse engineered and are more than a bit touchy. In other words, the problem isn't you, it is your hardware.

So what to do? I'd take one of two paths (both of which are much cheaper than paying Canonical):

1) Dump b43 and try the ndiswrapper driver. This is a driver that allows the use of Windows drivers in Linux and with Broadcom chipsets it has been pretty successful.

2) Buy a wireless card based on a different chipset. Intel fully supports their wireless chipsets and most distros will now be able to use them straight away.

Given that your wired connection has also croaked, a re-install of Ubuntu might not be a bad idea. If nothing else it might be quicker than trying to diagnose why the wired connection has died.

Thank you for your encouragement, Hangdog42. I will persevere. I am in fact going out of town immediately, without a laptop to use since my Inspiron does not have Internet access. (Sob, sob.) By midweek next, I should able to resume with your suggestions.
Yes, I'll reload Ubuntu first. Then try the ndiswrapper, praying. I hope I don't have to take the last resort of replacing the wireless chipset.
I'll be back. Thanks again.

Dear Hangdog42,
Going away for a few days seems to have done me good, for this story has a happy ending. It goes like this:
As soon as I could once back at hom, I resumed working on the phantom problem of no wireless connect. Dutifully I re-installed Ubuntu. The wired connection was revived. The system invited me to install close to 200 updates. Apart from Evolution related items, I let the updates proceed. These were the only changes on my previous Untubu installation.
Then it suddenly dawned on me that Ubuntu allows me to dual boot. That's good, I thought. When I don't have wired connection, I can at least run the factory loaded Vista that has wireless connection capability. I tried the Vista boot. It worked! I was so happy. Then I attempted Internet wireless. Dear, dear, Vista saw no wireless network!
How can that be? I clicked around and finally asked Vista is to diagnose why. It said, perhaps you didn't turn on the wireless security switch on the side of your computer (for security reason). I looked at the side of my Inspiron, and found, my Golly, the switch was indeed turned to off!
Right away I threw the switch, right away Vist a saw wireless networks. Suddenly I saw light at the end of the idiot's tunnel. Perhaps wireless networks were now also visible to Unbuntu. I rebooted to Ubuntu. Wow, indeed it saw the wireless networks without me doing anything whatsoever!
I kicked myself hard. I was such an idiot not to think of the switch, which I now recall playing with before I first installed Ubuntu. I wasted days working on the phantom problem that never existed; such a punishment I deserved. You and others wasted hours answering my questions; such a punishment you all did not deserve. Through my fault, through my fault. Thank you everybody for your patient help. Thank you, thank you.
I can't describe how happy I am. I just need to proceed to making Ubuntu see my Brother printer 2040, which, I hope will not be another phantom problem.

Postscript: Perhaps I should delete this thread, if I am allowed, lest other newbies read not right down to this happy ending and think ill of Inpiron 1525. Should I?