Jim, one more idea - do you have a bootable Linux or Windows Install CD-DVD? ANY bootable version will do.
Open up the case, unplug the power and SATA from the HDDs. Pull out one of the Mem Sticks, too. Then, restart the computer and let it sit on the Install Disk. Just sit there. Hours...see how it behaves.
If it continues to reboot, replace the Single Mem stick with the other.
If it still reboots, then you've got (1) Make sure all heat-sinks on the chipsets are attached...
(1) ReFlash The BIOS...
(3) Reseat the CPU (ugh)... this is probably #1 likeliest cause, by the way. Biting the bullet and doing this might solve all. Just pull it out, clean off the edges, stick it back in. Nothing fancier than that.
After that... "bad motherboard" would get my vote.