Without video there isn't much we can do on a laptop. In a desktop you could try a different video card, or different video card slot.
The only suggestion that I think may help is see if the computer will boot with taking one of the sticks of RAM out (assuming it has two). Does it boot then? If not, replace it with the other stick and try again. The idea is that two sticks of RAM usually don't go bad at the same time.
Without any video/being able to boot the BIOS we can't really run any tests
Generally if it was the hard drive you would still get the manufacturers welcome screen and instructions on what key to enter the BIOS. From there data can be recovered from the hard drive, hard drive diagnostics and/or software memory tests could be ran.