Just a thought: have you tried removing the battery and turning it on with only the cable attached. Removing the battery should be pretty easy, just by pressing two buttons on the underside of the laptop. Does your recharger cable have a little lamp light up when its plugged in? Does it light up? Does the laptop show its charging at all? Also: the fact that it doesn't turn, doesn't mean you won't be able to get your data back. If you get the money to repair it, make sure to tell the people that you want the DATA from it before they start working.
Oops ... uh if I have any more thoughts/ideas I'll PM you, sorry for going off-topc