Help! My computer won't start up

Last night my computer was working fine (though slow, in it's old age). Then it gave me a weird screen, it was gray but I could still see what I was working on, with a square in the middle saying that I needed to turn off the computer. I did, never thinking it might be a virus (my virus scan should be current), but now I am curious cause now it won't turn on.

It seems to be charging, and once in a while makes the "pop" noise that it always has when it's starting up, right before the screen turns gray but that is it. Other times it is just silent. I have no idea what to do with it or even where to start. I took out the battery and put it back in, but that's it.

Any ideas?

Hi Have you tried booting holding down the "option/alt" key?