Ok. I was able to run YaST Online Update, installing all recommended patches, including a kernel optimized for AMD processors. It warned that the NVIDIA installer needed to be done again, but I proceeded with the kernel installation. Upon rebooting, everything went bad. I can't even log-on in safe-mode. Here's some of the verbose comments during booting:

Using /lib/modules/2.4.20-4GB-athlon/kernel/fs/reiserfs/reiserfs-o
kmod: failed to exec /sbin/modprobe -s -k block -major-3, errno=2
VFS: Cannot open root device "hda2" or 03:02
Please append a correct "root=" boot option
You may want to retry boot with pci=noacpi or acpi=oldboot on the command line
If one helps please report with the following lines to acpi@suse.de
DMI: (hardware vendor info)
Kernel panic: VFS: Unable to mount root fs on 03:02

I tried the recommended boot options, but I still can't even log on. Does anyone have some advise?! I'd REALLLLLY appreciate it!

Yea let me guess, your root partition is formated as reiserfs, or not? You have problem! But you alraidy knew that. It think the problem is that your root partition is formated as reiserfs. To read that it needs the reiserfs module.... that is on the root partition. See the chicken and egg problem.
What should be done is that the reiserfs module should be compiled in to the kernel. You had that, of course, but yast scruwd that for you by installing an kernel that didn't have reierfs support build in to it. This is suse's fault and maby you should mail them to point out there is an potential problem for people.
Your in trouble Boot your system with the floppies from suse or with the boot cdrom. If I remeber correctly, there were two floppy's, one which was bootable, and one with kernel modules. If you boot form the floppy, the reiserfs module will be loaded from the second floppy (which the system will prompt you that you should insert it) .
If the suse bootdisks or cdrom don't work, try knoppix if you have that, or tomstrbt, which is an floppy based distro. Tell me if the suse floppies work or not. If they don't, I'l give you instrutions of what to do next.
Assuming you were able to boot the system with the floppies from suse, run yast again and re-install the old kernel.

Thanks for the quick reply!

I have no idea if my root partition was formatted as reiserfs or not, but sounds like you know what you're doing. There were more comments above that, but for now, let's assume that's the problem.

I don't have boot floppies, I have the CDs which came with SuSE 8.2 Pro. I went and booted from CD#1 and into the 'Rescue system' and was able to have very limited access to the computer. So, I need to run yast and re-install the old kernel?? How exactly, step by step, do I do that? If I have to reinstall the entire OS I will. This is my first home-made computer and there wasn't much on there before this problem. Thanks in advance!

He there.
So how limited is limited? Do you have internet connection? Do you have graphics?
Well the thing is, I know how to install an kernel, I have done it many times before. But I recoment you get an official kernel from suse, rather then the way I do it, i.e. go and fetch an kernel source tarball from kernel.org and compile it my self.
I don't know what you can run and what not, booting from the cd, but if you can run yast, see if there is an option for installing an kernel. I'm not to familiar with yast, so I can't tell you how to do that.
If you have internet connection, go to the suse site (www.suse.com) and see if you can get an kernel from there. I went there my self and I THINK this is what you need. It's an source kernel rpm of the 2.4.20 kernel. It will install the kernel source. After that, you will have to build the kernel your self. You do know how to install an rpm, do you? It's "rpm -i <package>"
It's hard for me to guide you through the build proces because I don't know what you need/want. But here is an document describing how to do that. If you do that, do not forget to compile reiserfs support in to the kernel!
Alternatifly, you could re-install your system, but I would recomment you try to safe it. What do you have to lose? And plus you will gain experiance.
Well, good luck and tell me how it goes.