Pc Freezes At Startup And Can't Get Into Safe Mode

HI, I have a PC problem I'm having a hard time figuring out and was looking for help.

I have a 2 year old HP Media Center with XP home. About a week ago the PC randomly rebooted twice. nothing had been installed or changed aside from a driver update for my video card about a week earlier. I tried a virus scan with trend micro, it rebooted. I started to back up some files on a USB harddrive and it rebooted.

I cleaned out all the dust and the fans work.
I ended up running the Windows Memomry Diagnostic ISO and the test came up with memory failures. (The test also ran overnight with no reboots, so I think that'd elimanate overheating) 2 1 Gig ram sticks. I replaced one of the sticks with a new stick, still failures. I tried the new stick with the other stick, no memory failures. So I thought I had it down to a bad RAM stick.
Ran fine for about 2 hours. I start backing up the hard drive to the USB harddrive and the screen went black. I reboot and it runs through scandisk and gets an unexpected error and reboots, runs through scandisk again, gets an unexpected error again, over and over.

I try running in safe mode and it hangs at mup.sys and will not go into safe mode. I went into the recovery console and did a chkdsk and it found an error, but doesn't detail what. I rebooted and it gets to the blue XP loading screen but freezes there. I ran the Mem Diagnostic test again and it's coming back with failures again as it had done originally.

So that's where I am. I can't boot up normally because it hangs and I can't get into safe mode. Any ideas? Thanks!

Some pcs i have worked with have done similar and it was a faulty power supply. Some one recently told me they one at a time disconnected various bits of hardware and found it was faulty cd causing the problem.

I also just had similar happen at home and I was able to do fresh windows install without formatting by booting up via an xp cd (this is always my 1st option in bootup). The hdd ran fine with this 2nd version. I was able to get into my old user account and take out bits i wanted and my other partitions were still there.

I went no further however as i rushed out and bought a new hdd which i decided to run with once I got the stuff i needed off the old one.