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Doesn't sound worth repairing, especially if the logic board is faulty. I'd sell it on eBay (salvage parts) and make your daughter get a job to help pay for a new one. Her fault or not, life's unfair and **** happens!

Get her a PC and see how many problems she has ;)
 
A logic board will run you $500 from ifixit.com and your time to put it in, and you still won't have a warranty.

Probably not a bad price vs the cost of a new Mac computer if you plan to keep it, but you should at least get a comprehensive diagnoses first, before spending any more of your money.
 
Send it in to MacService

MacService.com will do a full diagnostic on your computer and wont fix anything until you approve it... best way to find out what the problem is. With overnight shipping should take about 4 days...
 
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