ok, I'm going with the press&hold till it beeps multiple times approach. If that doesn't work...
...is it overheating in an enclosed space?? If so, put it in the open, let it cool for a few hours, try again while in the open.
...did you have a recent brown/black out or a lightning storm? Either of those could cause a power surge which can severely damage electronics. If so and nothing else seems wrong, sometimes homeowner insurance or power companies will cover the cost of damaged goods. Due to the low price of the PS3 though and being the only broken item you may not be able to collect on it.
... it could just be some other random problem and you should really just call Sony.