Mom and Dad have a Dimension 2400 that will not boot.

Problem started out of the blue.  No hardware or software changes were made prior to problem starting.  I've opened the case and double checked all connections.

Press the power button and Windows XP splash screen appears, it suddenly stops and the computer turns off.

I can press power button and as soon as Windows starts, I press F12.  Used option 6 to go into the Utilities partition and run diagnostics.  Everything tests as "OK".  One time I was able to boot into Safe Mode, but now I can't even do that.  While in Safe Mode, I set it to run CHKDSK, now on restart it attempts to run chkdsk but locks up at a random spot.  I say random because I've restarted a few times and let it start shkdsk, but it locks up at a different place each time.  Now I can't boot into Safe Mode.  Still able to press F12 and go into Utilities partition, but all the diagnostics still come back as "good".

Any help or advice is much appreciated.  Thanks.