There is a switch on the back of the computer that turns the power on. This works fine. But when I push the startup button to actually start the computer I get a beep and the LEDs flash but all power goes instantly dead. I checked the connections on the motherboard for the power supply and the front panel switches. These seem fine. Can I test the power supply itself? or what else can I do?

There is a switch on the back of the computer that turns on the power supply. This seems to work fine. But when I push the startup button the computer beeps and the LEDs flash on and off and the power just goes dead. I checked the electrical connections on the motherboard (main power connector and front panel switches). These seem properly connected. Any suggestions?