|See the info I pointed to !|
If your cpu fan and mboard capacitors / appearance check out okay, a failed cpu or mboard is extremely rare otherwise - the most likely thing is your power supply is failing.
Failing power supplies often still partially work !
The only way to rule out the power supply being the problem for sure is to try a known working power supply with your system, or, better still, to try your power supply with another working system.
Try another power supply that you already have on another computer if you can, or borrow one.
Your hard drives can easily be checked to see if there's anything wrong with the hard drive itself by connecting it/them to another computer, and booting the computer with a bootable hard drive diagnostics floppy or CD.
Check your hard drive with the manufacturer's diagnostics.
See the latter part of response 1 in this:
(thanks to Dan Penny for this link:)
Hard Drive Diagnostics Tools and Utilities
If you don't have a floppy drive, you can get a CD image diagnostic utility from most hard drive manufacturer's web sites, but obviously you would need to make a burned CD, preferably a CD-R for best compatibilty, on another computer if you need to.
If the hard drive itself tests okay, any data problems found can be fixed, one way or another.
If the hard drive itself tests okay, in this case, there's probably nothing wrong with the data on the drives.