Well, if you wanted to save money, I would start to figure this mystery out yourself. Count a freebie fix by Apple as out of the question (obviously).
Next, do you have any household or contents insurance which would cover the repair of the laptop? If no, read on.
Check with your school if they run a repair program for equipment students use for school work, worth an ask and a try. If no, read on.
You say the computer won't switch on at all. Now, which of these best describe the problem...
A) It won't power on at all, it is as if the life and soul has been sucked out of it by a langolier.
B) It won't power on from the battery
C) It won't power on from the AC power adapter
I know those are a bit obvious, but worth asking (sometimes people try to power up using one method)
Things I would look for if it was my laptop...
1) Check the battery fuel lights, do any light up?
2) If you can, check the power lead on another Macbook, is it still functioning properly?
3) Is there any life at all when trying to boot up? can you hear the hard drive or optical drive kick in?
4) which status light does the magsafe show when it is plugged into the laptop and the battery is in?
If the thing is as dead a s a do-do and you know both the battery and power adapter are fine, then it must be a problem with the power part of the motherboard, as if any power was getting through at all, there would be a kick out of the hard drive, screen, or optical drive at least.
if it is the power bit (sorry i do not know the exact name of the part) of the motherboard, then it would seem like it needs a new motherboard, and that would sort of reflect the cost of Apples repair quote.
I don't know if you have the eqivilant of
www.thebookyard.co.uk in the USA but if you do, it would be worth buying a second hand motherboard and fitting it yourself.
The extra cost is in the labour involved as replacing a motherbaord in an apple laptop generally means taking everything out of the case, putting in the new motherboard and then re-=attaching all the internal peripherals to the new motherboard.
A task not for the faint of heart, but it can be done.
www.ifixit.com should have the step by step pictured procedure on their site. Oh look, here's a link...
http://www.ifixit.com/Guide/Mac/MacBook-Core-2-Duo/Logic-Board-Replacement/116/19/
Mind you, having looked at their replacement parts list, it might also be the magsafe board...
http://www.ifixit.com/Guide/Mac/MacBook-Core-2-Duo/Magsafe-Board/116/11/
beating all that, what I would try is to find out about someone who is just plain good with electronics. Someone who quietly repairs peoples broken stuff because they enjoy it. This sounds like a job for someone like that. The internals of the macbook are relatively simple and your problem sounds like a relatively simple one, I.E. no power gets to the parts that need power, and possibly someone good with electronics could track where the power stops and therefor work out which component is faulty.
I know this may not be a big solution, and chances of someone coming forward and saying they had the exact same problem and found a fix are slim, but I hope it is some food for thought.
Mel