When I turn on the power of my computer it only turns on but won't boot up, it won't even make the post boot beep. I haven't installed any new hardware. It just started doing that recently. It boots up after a number of turning off and on. What could be the problem, how do I fix it. Its an Acer veriton M460 with a celeron A procesor.

When it doesn't boot, is any video displayed?

My usual procedure for no boots:

Verify power path from wall outlet to motherboard with power supply tester and multimeter.
Disconnect power cord, remove memory, dust out memory and expansion slots, and reinstall memory.
Check CMOS battery.
Disconnect all the drives and remove all adapters and see if just the motherboard, processor, and memory will POST normally. If they do, one of the removed devices may have an issue that is delaying POST completion. If they don't, stick in a POST card (http://en.wikipedia.org/wiki/POST_card) and see where POST is hanging.