Cpu heatsink fan fell off while launching a game

If you get beeps when you turn it on thats a sign that the cpu is not dead and there is another problem. In fact, take out all cards, memory, disconnect the drives and turn it on. If it doesnt beep then you probably have overheated the cpu or the motherboard is damaged.

This is assuming the power supply turns on when you press the "on" button

As said above, the system should at least beep.

the cpu "Should" shut off before it overheats. But a heatsink falling on the video card is never good.

disconnect everything, just leave power to the board one stick of memory and the video card. Try to boot that way, see if it posts(with no drive plugged it will not go to windows, but at least you will see if the board is working).

You may also want to look at getting a video card off a friend to test. After all a heatsink falling on the card may have shorted or otherwise damaged it.

If all else fail, you may have damaged parts and it is going to take some time to test all parts on another system and see what was damaged.