My laptop did something like that. Turns out that, with mine, there's a loose connection between the motherboard and the monitor (or something like that). The only way I could get an image was to press on the screen in two of the corners. It's only a temporary "fix" though, unfortunately.
Heh, I'm kinda having the same problem with my HP Pavilion laptop... I haven't had a charger for a few months and my computer was having this problem before my last charger died but now it won't work at all... it'll turn on and I can hear it running, but I hear no sounds and the screen is black... then it'll restart itself after a few moments, and it'll just keep doing that until I unplug it and take out the battery. x.x It won't do anything.
I really have no idea what to tell you since I don't have any suggestions for myself... LOL. But, good luck!

My Macbook was doing something a bit similar; it would start to boot up but then it would make these crazy beeping sounds and it wouldn't finish booting. Turned out that I needed new RAM or something. Slim chance that you have the same problem though, and mine had to be fixed by Apple Geniuses, so... :P
Rhiannon - could be the monitor, but I adjusted the screen/pressed it etc. before to check this and nothing. :(
JazzehChan - that's really weird! Hope you get it fixed soon. :x
Sammii - it could be that. It doesn't make any crazy beeping sounds though. =/
I was thinking I could run the Apple Hardware Diagnostic Test CD but obviously I can't turn on my laptop to put it in. -fail- I managed to get it up yesterday though. When I do manage to get it up it works absolutely fine, like there's nothing wrong with it. So I made use of it yesterday and watched a DVD before shutting it down again. And today I tried it many times but to no avail. :(
I really want to open the whole thing up and try and find out the cause, but I'm too scared. xD I've lifted up the keyboard before - to fit an airport card - but I'm too scared to fully open it up incase I break it even more. x_x!