It sounds like you've eliminated everything except the motherboard. Make sure that the motherboard has a proper ground and is not being improperly grounded. I've encountered two cases prevously, the first was whoever assembled/rebuilt the PC used plastic standoffs for ALL of the mounting holes on the motherboard. The board did not have a good ground reference (a more or less floating ground) and after awhile the computers reference voltages would migrate and it would start doing really weird things like locking up, rebooting, emitting strange sounds through the speakers, random floppy disk/cdrom activity, etc.
The second case (actually had more than 1 instance) was where the motherboard had too many ground points. In one PC it was discovered that a drive mounting screw had fallen out and had lodged between the motherboard and the chassis. The vibration of the PC during normal operation would cause the screw to shift slightly or expand due to heat and basically short out the motherboard causing a reboot. In other instances, again goes back to whoever assembled the PC, it was found that there were too many M/B standoffs. The standoffs were used in places where no standoff was engineered to go. Removed the extra standoff(s) and the PC started acting normal. Unfortunately, I wasn't able to save a few "patients" as the extra grounding components rested against something critical and smoked the board.
Another tip, carefully check all of the data cables going to your peripherals (hard drive, floppy drive, cdrom drive(s), zip drive, tape drive, etc.). Again, I have seen where the person who assembled the PC passed the data cables through an opening in the chassis that was sharp. As a result the insulation was nicked or removed from the data cables. During normal operation the cables would vibrate or undergo heat expansion and ground themselves against the chassis causing a lock-up or spontaneous reboot.
Barring all of that, is the PC flashed with the latest BIOS revision? If it isn't I would recommend doing so. If it is, you may want to try to find the previous version and "downgrade".