Any ideas as to what specific component to replace rather than a $hotgun approach?

While nearby, I happened to observe my desktop suddenly crash. It was on but had not been used in an hour or so. It would not POST. No beeps.

In more than 50 re-start attempts, it successfully POSTed then went on to successfully start Windows once. On 2 occasions it began POST then stopped with the message: CMOS check sum ERROR, defaults loaded. Warning! Now system is in Safe Mode.ter POST.

On all other tries, nothing on screen and no beeps.

Have tried to follow the many troubleshooting guides on the website.

Fans and hard drive seem to spin normally.
Peripherals/Drives have been removed.
Memory has been removed and rotated in all combinations.
Motherboard battery replaced.
CMOS had been cleared with motherboard JUMPER several times.
With CPU fan removed, CPU became warm within seconds.
F8 and Del keys have not had any EFFECT when turning on.
Monitor works on notebook.

The home made machine gets pretty light use, there has been no gaming, intensive graphic use, etc. It is 3 years old.

G-Force 6600 PCI Express with 256 MB
Biostar N4SIE-A7. SLI not hooked up.
Windows XP-professional, with antivirus –all up-to-date
Ultra ULT31849 X-Finity 600W Power Supply
Intel Pentium 4 630 Processor Prescott 3.0GHz, 800MHz FSB, Socket 775, 2MB Cache
DELL 19” 1905FP
Kingston (2) 5300 (1 GB DIMM) INSTALLED.

Thank you in advance!
Try it with only ONE stick of RAM...installed in the slot closest to the CPU...
Borrow a known good PSU of the same or greater wattage and swap it in there...
Replace the CMOS battery (even though you have already done so...i've seen them dead out of the package)...Installed 2nd new CMOS battery. Used each memory stick independently in each slot. No change -no POST.

Don't have a PSU substitution option until I buy another. The 600W unit is oversized for my use -doesn't mean it didn't fail. Any way to check? Volt meter shows up to 12V (depending on pins -can't reach them all.

Thank you!check to make sure all molex connectors are in tight
reseat the ram
take cmos battery out and unplug power of 2 mintis
put the battery back in
turn it on
see if it POST'sTried all of your suggestions without any POST activity that I could discern. Thank you for your ideas.

Seems to me that it could still be MOBO, CPU, or PSU. We have probably ruled out RAM. The PSU seems unlikely to me.

Originally, I thought I would be faced with a few hundred bucks to modernize the PC when it met my needs as it was. However, on eBay for a $100, I found a compatible used MOBO with 2MB of similar RAM and a slightly faster CPU combo so I will try that route.

If I discover the issue I post the finding.

Thanks again for help.