most times its the power supply, you will notice that the power button on the front is orange instead of green. That model i found is also very fussy about ram, have you installed memory recently?
another common problem with that model in the small form factor is blown capacitors on the mobo.
This was actually a prevalant issue on about 5 different model Optiplex issues which also prompted a pro-active motherboard replacement campaign through DELL. I remember when this was first discovered.
@OP: If the computer is still within warranty or closely after expiration, contact DELL and let them know that you potentially have "blown caps" on your motherboard and they will likely send someone out to replace the motherboard.