rebooting PC

Clarifications

the fan in the power supply died.

It might be possible that you're exceeding the capacity of the power supply.

Using the same type of RAM, but made by different manufacturers gave me problems once. The RAM tested ok repeatedly!

Look on your system board.
Check out the capacitors. If any of them are bulging that could also explain the rebooting. If this is the case than you need to replace your system board.
This was common on both Dell and IBM computers.

See this site for an example.

http://www.tnpcnewsletter.com/dan/Bulging_Capacitors/

When the PC is moved or after years of use, the thermal grease may no longer make contact between the heatsink/fan and the CPU. Enter the BIOS, if possible, before the computer reboots, and look for the CPU temperature. Around 80 C, many computers reboot automatically to avoid overheating damage to the CPU.

Many bio's have a setting for the temp to shut down at certain temps. if this setting is too low, it is easy to hit after a while, especially with older AMD.

Have you also tried blowing the system out and making sure the fans are all working properly?