My 1.4 athlon started doing the same thing about a month ago and it got progressivly worse. At the moment its in pieces. First I thought it was a powersuppoly problem but changing cases soon told me i was wrong. Theres a small crack in one of the tracks on the motherboard caused by prolonged exposure to heat, thanks to being switched on 24/7. I will buy another board for it soon but for now i have to use a shitty old 433 for my Gateway
Check the Ram, see if its in the sockets properly.
Check the power supply. If its an AT case, just unplug the motherboard completely and leave it of to see if it turns itself off after a given time!
Check the Power button. (ATX CASE) unplug the power button from the mother board and use a screwdriver to short out the pins where it pluged in to turn it on. Wait to see if it turns off again!
ummm... maybe examine the motherboard for signs of cracks and scorch marks ect. The motherboard CD may have also come woth a diagnostic program that checks if the board is functioning properly.
If ya Need a CPU to get ya buy for a while, let me know, i have plenty of old systems lying around.
Good luck man, hope i could help.