Have you checked for bad caps? (here is an example of what to look for: http://www.badcaps.net/)
I have seen this more times than not when a capacitor goes bad you can get some really strange issues...
What about overheating? Does this happen if the PC sits turned off for a while then you power it on? Or does it not matter the environment prior? Could be a bad cooling fan/setup. What about thermal paste on the processor?
That's a thought. Remember there are capacitors in the PSU as well, but you might not be able to get into it.
Is there a warranty on this box by any chance? Stupid question but you should always check that first..
I agree that it sounds like a PS or heat issue but I ran across this and thought it might be worth looking at - hard to tell from posts if the notebook will boot to CD. http://www.winxpfix.com/page18.htm.
That solution requires the machine to boot as far as the Windows logon and to read the CD/DVD drive.
From the symptoms described, what we seem to have here is a hardware problem not an operating system one? The real issue is that we cannot get far enough into the boot to get to a CD and run diagnostics.
That suggests a PSU or MoBo problem to me.
1. It isn't the hard drives because we don't get that far, and we would be able to boot from a CD.
2. I don't think it is the video card, as when they progressively deteriorate you would see weird display problems, not boot-up ones. What should happen is the machine would still go through the boot sequence but give a black display at the end. I would also expect to get BIOS beeps if the video card or RAM were faulty.
3. My approach would be to test the PSU then fully charge the battery and try it on battery power only. If the PSU is OK and it won't run off the battery, then it is almost certainly the MoBo.