Yeah...it wouldn't even need to be running to be damaged by an impact....but it does increase the odds.
If you'd like to test the computer without a hdd I'd suggest running a Linux live cd. That's probably what I'd do. That way you could verify the DVD drive as working as well as the memory.
When you are in the bios, does it see the hdd? And the hdd, is it an ssd or an old school mechanical? When you are trying to boot from a cd did you make sure to set it as boot first?
Just wondering why you don't seem to suspect the hdd at all...