Are you sure it is the logic board that has gone?
Reason I ask is, my 2010 MBP started having problems booting to OS X. I thought it was a dying hard drive. But checking the drives showed it was working. I was worried about it being the motherboard starting to become faulty, but after looking around t'internet, I saw a couple of posts on a few forums that said I should try replacing the SATA cable before thinking about buying a logic board or going and paying for Apple to replace it. Did it with a supposedly genuine part (the replacement part is actually shorter than the original, so just barely reaches) and it's fixed (typing on the MBP now).