OPTIPLEX 390 wont stay on

I3-2100, 3.1, 3MB, SNB, 65W, Q0

one 4G DDR3

given to me as dead.

Powers up but would not boot up. Blank monitor. Cant get into Bios. It powers down by itself after seconds, tens of seconds, minutes, or tens of minutes..Tried this many times.

Moved ram to other slot and it booted to Bios and windows. If it stayed on that long. After a while it shut down again by itself. Tried this many times.

Swapped out HDD, power supply, and ram one by one with known good. Problem remains. That is it boots up, then powers down by itself after seconds, tens of seconds, minutes, or tens of minutes..Tried this many times.

When ever I plug in a power supply (tried several), it starts up for a few seconds, then powers down. Once it did not power down for several minutes. Once while looking at it, it powered up all by itself.

While powered up touching/wiggling the power button does nothing.

ideas? Im guessing the board is toast. Might the processor still be good? Will this processor fit into a optiplex 380?

tks,

paul