Compaq presario 2500 notebook won't boot

OK, here's the background with this computer.

This laptop has been "shelfed" for about a year now, but the other day I decided it would be handy to fix. I'm a poor college student so I don't have to blow sending this to a shop somewhere, and I'd like to get it working again. The original problem was that it wouldn't (usually!) boot at all - it seemed to be completely dead. I would plug it into it's a/c adapter and press the power button, but NOTHING would happen. Occassionally, like once every ten minutes or so, an orange led light in the front would flash a few times. (the led with the thunderbolt symbol, I think it's the "battery charging" led) What was strange though was that sometimes, for reasons beyond me, when this orange led flashed and I pressed the power button, it would SOMETIMES boot up into windows and run perfectly. But this was only like once every 30 mins or so - I had to fiddle with it for half an hour to get it to boot. The trick where you remove all power sources and hold down the power button then tried to reboot worked a few times, but then suddenly quit working and the computer wouldn't boot at all - not even after fiddling with it for half an hour.

I was pretty sick of this so I took it apart and wiped some dust off the heat sink. Everything looked OK so I put it back together. Now, I have a new problem. When I press the power button a bunch of blue leds light up and the fan kicks on, (whereas before everything but one orange led was completely dead) but there's no display and nothing boots. Anybody have any idea whats wrong?

(on a side note the battery is dead, and i've tried everything I've with with the battery in and out)