Quite possibly it is a bad contact on the RAM.
Oxidisation causes a bad connection.
Pull the RAM out and clean the contacts with a pencil eraser.
My experience has been that if you press the power button, all the lights come on, but no "beep", then it's a bad contact on the RAM.
You don't necessarily get an error code beep.
In some cases bad contacts on the video card causes the same symptom.