I thought I would relate this story for future searches and because I couldn't find anything anywhere that would have lead me to this conclusion.
I have a 5 year old HP computer. All the pertinent specifications are listed under the "HP in basement" computer in this post. This computer started to lock up and random intervals, weeks apart. This was not a BSOD or some program related lockup, either. I'm talking about a full, nothing-but-turning-it-off-works, lockup. After 3 or 4 of these, the computer locked up and, upon reboot, displayed the error message "S.M.A.R.T Capable but command failed" for the Primary IDE Slave Drive at BIOS startup. Proceding past this step would result in XP attempting to boot but just sitting and running the slider but never getting to the login screen. After rebooting in SAFE mode, turning the computer off via XP, and starting up again, everything was normal. About 24 hours later, this exact same lockup process was repeated. At this point, fearing that I had a failing hard drive, a WD Caviar 500GB EIDE, I downloaded and ran the WD SMART diagnostics. None of the tests produced any failures. Not wanting the hard drive to fail before I could get the remaining data off of it, I unplugged the hard drive power and the 80 wire IDE cable. After unplugging the hard drive, the computer operated flawlessly for 72 hours. I was beginning to think that the hard drive was indeed the culprit when the power supply failed completely and the computer would no longer turn on at all.
So, the 3 year old Xion LC-B450E 450W ATX supply gave up the ghost. I replaced it with a new OCZ 500W StealthXStream, plugged everything back in and it has been running flawlessly for 36 hours. I run WCG in the background so this PC is always working. A big thanks and thumbs up to pipemanid who suggested checking power supply voltages. Apparently, the new 500GB+ 7200RPM and up hard drives are extremely sensitive to voltage fluctuations.