Maybe you can try resetting the SMC chip's settings which controls all the power up and power down (this is nothing to do with the PRAM). Turn the computer off and disconnect all cables, including power cable. Wait a couple of minutes, plug the power cable back in and power up.
Interestingly, I had the opposite problem today: my i7 iMac refused to startup after having had a power outage while it was asleep. I pressed the power button and the hard disk, fan, superdrive get power, but no startup chime, nothing on the screen. After doing SMC reset, I had to power on by holding the power button down until the startup chime came. It worked. Weird....