I was having some trouble with my Mac Mini after doing a firmware update. After trying to reboot there was no video at all, just a black screen with a white box. It would make the chime sound when I tried to restart it, so I knew it was still alive, but I couldn't see anything... and it's pretty damn hard to do anything on a computer when you can't see anything.
If you are having the same problem I was having, you may need to reset your Mac's PRAM. You will lose some settings but that's a small price to pay for having a working computer again. What you need to do is try to boot up the Mac and as soon as you hear the chime sound press Command+Option+P+R if you have an Apple keyboard, or press Windows+Alt+P+R on a Windows keyboard... and once you press those keys keep them all pressed until you hear a second chime. If you have no video, it can seem like nothing is happening, but be patient... don't let go until you hear that second chime or this won't work. Eventually there should be a third chime, and then you can just boot normally.
Depending on what problem you are trying to fix, if resetting the PRAM doesn't help, then you might want to also try resetting the System Management Controller. There are different ways of doing this depending on what kind of Mac you have and how old it is
And if that doesn't work either, you are probably screwed... at that point I think you will pretty much have to make a trip to an Apple Store to get it fixed.