Computer Keeps turning off and on (No Signal Monitor)

Hi,

I'm having this prob for a while,
When I start my computer i can hear the fan turning, and lights and shuts down automatically without any start up signal on the monitor.
When I remove the VGA cable and connect it back I can see the monitor displaying sleeping mode.
But then no start up signal.
I move the VGA for many times before the computer starts.
It takes me too long before it start (20min).
Do you guys have any idea what could be the problem?
I changed the VGA cable as well. Still the same problem.