random BSOD hardware problem?

Bootdisk.Com - has all sorts of boot disks for free

Yes, but you'll have to read up on how to do that.

So I tried running Prim95 and my machine blue screens immediately after starting a test, does this narrow it down to a cpu problem?

No, but it does make it pretty sure that you've got a hardware issue.
Now you've gotta decide how to spend your money.
A replacement CPU or a replacement motherboard (or a new system?)

You could have caused the damage, a power surge could have caused the damage (even with a surge protector under certain circumstances), or it just could have died.

If it's been less than a year, could the parts still be under warranty? Either from the reseller or the manufacturer?

Here's some steps that may help w/hardware troubleshooting: Hardware Troubleshooting Via System Stripdown

It's unfortunate, but there just aren't any tests that you can run (other than hard drive and memory) that'll tell you if your hardware is OK or not. Even the diag's that Dell builds into some of it's systems aren't a thorough diagnostic.

Stress tests, like the Prime95 program, will cause your system to crash (which is sort of a hardware test) - but that doesn't give you a firm decision for purchasing parts.

There's 2 ways to fix computers:
- do it yourself
- have someone else do it

If you do it yourself, you're bound to accumulate a lot of spare parts over time (I've got 5 older, retired computers at my house - along with the 9 working ones - and an attic/work area full of spare parts).
If you have someone else do it, they'll have accumulated the spare parts already - but they'll charge you for the testing.

Good luck!