Hullo Again... my sincere apologies for such a l-o-o-o-n-g delay in replying to your earlier suggestions. A family emergency called me away interstate for nearly 3 weeks - and I've only now been able to spend a bit of time working through your various suggestions.
Interesting development since I started using my system again though: I started getting some (very intermittent) error messages on boot-up telling me that my system memory had changed! The messages would show that I had somehow dropped 500KB since last use - which of course was not strictly true. And the BIOS Setup showed all four 512 KB memory sticks installed and working - even though it said I only had a total of 1.5 GB memory installed!
So I decided that it was time to do the hardware rectification thing you suggested - and set about giving the insides a thorough cleaning. I also re-seated each of the memory cards. There was a bit of dust around the fan inlet and between the layers of the (huge) heatsink on my CPU... but nothing really scary. Nevertheless I got rid of everything I could see and the CPU is now running at 51° (Celsius) as I write. Intel says the maximum working temp for this CPU should not exceed 70° - so I guess I don't have a major overheating problem.
The memory modules have now been removed and re-seated (an awkward job on a Dell 4700) and I must say this could well have been the problem. When I first released the catches a couple of the cards immediately sprung loose - which indicated they may not have been properly installed. I've now fixed that situation.
All that remains now is to wait and see if these remedies have solved my BSOD issues. So far, so good... but it's early days yet!
Thanks guys for all your help and patience. I really DO appreciate everything you've done for me - VERY much!

51C is still high for an idle computer.
What did you use to clean the computer?

Long delays don't bother us. In fact there are a lot of people who don't bother to reply either way. By the way,

Originally Posted by Digerati

You probably have more memory than that in your watch! Try 2Gb, 4 x 512Mb -

I really hope that this is a mistake on your part. Windows couldn't run on so little ram.

Ok on the over heating, what you need to look at isn't mainly what your computer idles at but what it is at under heavy demand so before we rule that out, please install and run prime95 for at least 30 minutes and then tell us what the typical as well as peak temperatures are while running prime95. If you need to have speedfan log the temps. You should also be able to add a fan or two if need be unless all of the spots are taken.

Although heat could be an issue your memory concerns me especially since it isn't recognizing all of it. Did you buy the ram your self or did it come from dell? If so are you sure that the ram matches the computer's requirements and that they also match each other? That is very important. I would try to run the memory test again and preferable one from the manufacturer. If they are still under warranty I would try to contact their technical support.

One thing I thought of is that you can test 1 stick of memory at a time to to see if your computer recognizes them all. If there is one that isn't I would test it in all of the slots. If it still isn't I would leave it out and test the rest. If no BSOD I would suspect that the stick is bad. If all of the sticks are recognized by the BIOS individually I would suspect a conflict between the RAM or issues with the motherboard. If you can isolate the memory to one stick and you leave it out and you still have a BSOD I would suspect either a driver problem or a problem with windows. Take note of what if any driver it lists and what error code that you get.

OOPSIE (again!) on the RAM size. Sorry about that. (Why do I keep making this mistake I wonder??)
Now - dealing with everyone's helpful emails. Thankyou all for your support.
First - I used a can of compressed air to clean the internals. It worked fine.
Second - the memory cards were partly installed by Dell and partly by me. The machine came with 1GB factory installed... I used the Crucial Memory Tool to identify the right memory type for the upgrade. Once this was done I purchased the the additional 2 x 512 MB cards direct from Crucial. The installation was done nearly 4 years ago and everything has worked just fine since then - until this message started appearing a few days ago. However since I removed the cards and re-seated them there doesn't seem to be any problem. I've done the memory diagnostic test again - AND the single stick test - all OK. (The BIOS setup also recognises 2 GB of RAM now... so I really think the problem was a card that had worked its way loose.)
Third - Yesterday I ran Prime 95 for nearly 6 hours continuously. The system passed every test without a single glitch. Typical temperature during the test was 52° - 53° and the one peak (right at the end of the test) was 57°.
Finally - I haven't had any BSOD's for the last 3 days! Touch wood!!!

Yes a mis-seated chip probably would cause problems so lets hope for the best that that is your only problem. 52-53 with a peak of 57 is pretty good for a torture test. You didn't have to run it for 6 hours though; 30 min to an hour should have been good enough. I would have suggested that you remove the sticks that you bought to see if it worked without them but if you did it 4 years ago with mainly no problems I'd say that you matched them up nicely. Well let us know if you have any more problems.

Thanks a big heap townsbg. I surely WILL come back if any further problems occur!
And thankyou also Broni and Digerati for all your help. You have nursed me through this difficulty very carefully - and I really appreciate it. (Of course if either of you have anything extra to add to townsbg's remarks I would love to hear from you.)

I'll send my mindump.zip file too

Originally Posted by triin1

I'll send my mindump.zip file too

Ummm, why? Do you have a problem and if so what? Or is it just because you want someone to look at then? If you don't have a problem then their isn't really a reason for us to look at them. You haven't given us any information.