It also happens to me after the sceen saver work, and particularly after my daughter plays on line games.

You don't say what projects you are attached to, or if you have noticed that one particular screensaver is related to the issue - but there are several possibilities, or at least things to check. (I personally don't think the problem is BOINC-related, as I've seen similar cases too many times where BOINC wasn't installed at all, and if there were some major bug in BOINC, with a quarter of a million Windows installs, I think it'd be more obvious...)

1) If the problem happens when the Einstein screensaver is running, and you have an ATI graphics board, there is a known bug that causes Einstein WU errors. No reports of it affecting Windows however, unless the crash is in the graphics card drivers (generally requires them to be several versions "behind" current).

2) One easy way to determine if the screensaver is contributing/causing the problem - turn off the screensaver! Use some simple boring one, or even "blank". See if problem continues.

3) If problem does continue without the screensaver, remove BOINC from the list of startup items. Run without it for a couple of days and see if you still have the problem. If not, begin running BOINC manually after startup, and exiting it before doing anything "heavy" (games, etc.) and see if you begin having it. Finally, still starting it manually, let it run continuously, and see if problems resume.

If you can narrow down the cause to a certain combination of "BOINC was doing this", we can possibly figure out how to solve the problem. Or, if the answer is "oops, BOINC had nothing to do with it", then you will have a direction to look to see where the true problem is.

I downloaded the highest version number client just before Thanksgiving (5.2.8) and have tried to run it for seti@home at default settings.

It's up to 5.2.13 now. If you have any connectivity or networking issues it would pay to go to the latest as they seem to have finished the current round of bugfixes. Basically, stop BOINC and confirm stopped, install "over the top", and then restart BOINC. All work in progress will be preserved.

However, every time I return to my computer after BOINC has run, the system hangs and then crashes to the BIOS soon after

Not really sure what you mean here. I've looked you up at Seti and you have quite a list of successful results with no signs of client errors. If BOINC were crashing your machine I would expect to see some "Client errors" in your results list. When you say "after BOINC has run ..." do you mean that everything is OK while BOINC is running but if you stop BOINC then soon afterwards, the machine crashes? If so, I've never seen that before. Can you capture any unusual messages from your BOINC Manager message window? How do you start and stop BOINC? Can you give a lot more detail on how you use your machine and what is actually going on just before the crash?

So what is going wrong? Is there a bug? Do I have something set improperly in the options? I very much want to continue to help projects like SETI, but not at the cost of an eventual hard drive reformat or failure.

I've not seen anyone else describe problems like yours and I'd be surprised if it actually is a bug in BOINC. I think it's more likely to be some sort of hardware issue under load. Can you try some other system stressing software like Prime95 to see if your machine really is stable?