Note that I'm not trying to favor Ubuntu but with regards to the root access it's fairly easy to achieve it in Ubuntu (and I guess in other distros that favor sudo over straight root access). That is what the first step below does. The second step applies to all distros that do not allow access to the graphical environment.

If I remember correctly:
Step one will enable root login in a console by simply setting the root password.
If required, step two will enable root access to the graphical environment by editing one line in a config file.

A little research here or on the rest of the internet should tell you what to do exactly.

No Internet at home,

then I would again recommend Debian and suggest you download the full 5 DVD's so you have local access to all the packages.

Mandriva 2008, Mint5 and above, will do.

Fred.

My thanks to those of who have responded to my post, especially to those who have provided suggestions to distros that might meet my needs. I will give consideration to every suggestion, and consider how I can best move on in my Linux experience.

I should mention that I have only been using Linux since February this year although I had been a Windows user for many years. So, although I am no longer a freshly-minted Noob, but there are still many basic skills that I need to pick up, and and learn how to apply, to achieve my needs. I recognise that this lack of experience and knowledge on my part has had a large influence on the six requirements that I initially specified. To some degree they represent my impatience in wanting to find a faster way of becoming more proficient in using this new operating system, but at the same time I also recognise that most worthwhile tasks have a steep initial learning curve.

That impatience is partly exacerbated by the knowledge that many of the tasks that I am currently struggling over ar present, I would be able to do easily in Windows. However, I recognise that if I keep falling back on what I already know then I will only slow down my progress in becoming more proficient with Linux.

Thanks also to those of you have mentioned other ways around the issues that I am facing. I will also try to research those methods to see if they will work for me.

Only if you have a decent 'net connection. Otherwise use the net install option.

Then again I'd go with Mepis ....

You must have misread the post, he has NO internet connection at home(see post #8), that's why he should get all 5 DVD's up front..

Using a distro with a light install (1CD or a netinstall) where he needs to hit internet repositories to get any software will be painful, as opposed to having tons of the software available locally on DVD. .

Eleven distros in five months? That may be some kind of record!

I think you need to slow down and stick with one. It's not so much a matter of finding the ideal distribution, as of getting to know a reasonable one and then tailoring it to your needs and habits. I'd back the suggestion of Debian. Get the five DVDs of Lenny and you've got everything to hand. The media codecs are easily obtained. Lenny is stable if not cutting edge, and you can safely get a more recent version of anything critical.

Maybe it's like being a kid in a sweet shop?
To re-arrange windows you have to look far but to do that on linux/unix it treats you like a grown-up.
Maybe the biggest contrasts are between Gentoo and Mandriva, set 'em up on Virtualbox.

Fred.

A big thanks for all of your contributions.

My inclination at this stage is to try out Debian for a while and see if it meets my needs. I was also very tempted to look at Gentoo, but I believe that I do not currently have the skills or knowledge that would be needed to use it properly.

For those who wish to know, my decision was based on the following:
(1) I recognise that I can't just keep jumping from one distribution to another, and I need to settle on one, at least until I get a better grip on the fundamentals of Linux. DavidMcCann's comment
was a bit of an eye opener to me. I hope that there are some users who have gone through more distros than this, as I certainly didn't aim for any sort of record. Also, as I have already said, the quick turn around of distros should not be seen as a criticism of any of them. All of the distros that I installed were good, and to be truthful, I would be happy to use any one f them. I am just fortunate enough to subscribe to a monthly Linux magazine that comes with a DVD that contains at least one recently released Linux distro, and so I kept tying them out.

(2) I can get all (or at least a large amount) of the software in Debian's repositories by purchasing the 5 DVDs, and without having to trying to download this from a website without benefit os any sort of package manager. Because of my current inability to get internet access at home, this is a very strong selling point for me. I understand that people who have internet access may not put the same priority on this requirement as I do.

(3) The ability to easily change configuration files in Debian is a big selling point. I believe that I can learn more from an operating system that will allow me to make mistakes rather than one that tries to anticipate mistakes I might make and prevent me from making them. I accept that many people will view this matter differently, and possibly, after I have had to fix up my umpteenth mistake, I will prefer a distro that is more proscriptive.

Also, for the record, there are a couple of things with regards to Debian that I don't like, (but I am prepared to live with):
(i) I would have preferred a distro that was using KDE 4.2.
(ii) I would have preferred a distro that was using a later version of Open Office.
(iii) I would have preferred a distro that had a better record for getting it's updates out on time.

I think that you wouldn't actually prefer that; it looks good (but not to everybody), and you would think that its what you are going to like, but the actual experience of using it isn't exactly pleasurable.

Firstly although its immeasurably better than earlier versions (and think how bad that means that they were..but I'm not suggesting that using 4.1 instead is a good idea), it still has a fair measure of frustration. There are people who will like this kind of thing, but suggesting it as someones introductory experience of Linux doesn't feel to be doing them any favours.

And you'll find that over the next couple of months you'll be doing very frequent updates, some of which will break things that used to work, in the desperate hope that you'll get a version that doesn't have serious irritation potential. Whether this is even practical without some kind of access to the internet, I don't know (maybe you can use a library, or someone else's, occasionally).

I shouldn't be completely negative about this however; you'll learn.

I too second salasi's thought on KDE 4.2. It has become a bit too bloated and complex. To make it more colorful and eye candy they forgot to make it useful and useful for new users as well. It takes a lot of time to settle down on KDE 4.2. It has become more of Vista kinda thing.
In contrast Gnome is really nice and systematic. Though not lot of eye candis that are available on KDE, it still keeps itself simple and more usable. Debian with Gnome is a nice choice.

Well if you are getting DVD's from somewhere.. you could always grab the Debian Squeeze DVD's

http://packages.debian.org/squeeze/kde-full
KDE 4.2

http://packages.debian.org/squeeze/openoffice.org
OpenOffice 3.0.1

Squeeze Weekly Build DVD's
http://cdimage.debian.org/cdimage/weekly-builds/

No it's not completed yet it's still in the testing phase, but it is still pretty darn stable.... just a thought