The startup sound won't happen if, the last time your computer was actually on, you put it on mute. If you put your Mac on mute it stays muted when you turn it off.
You could try holding down the power button for longer than seems natural. Also try attaching an external monitor--that's one way to find out definitely whether it's the screen.
Another screen-related thing is (really) to hold it up to a window or something so that light shines through. Unlike CRT screens, LCD screens don't give off any light of their own; they have a backlight which can go out. (That's, incidentally, why displaying black on an LCD actually uses up more power than displaying white--you're shining a light and then using the LCD to block it.) If the backlight has gone out you can still sort of see if the computer is booting up if you shine some light through the screen.
You probably need to take it in to an Apple store if it's not the screen.
(Also, I say this every time someone has a computer problem, but there's no reason anyone should ever lose any data to a computer problem, ever. Big files and shit should be backed up through something like Time Machine. Small files can instantly be backed up online through something like Dropbox. Everyone should have everything 100% backed up always.)
