Liquid damage - Can't power on when unplugged
I've got a MacBook Pro that received a coffee bath. Everything seems to be functional aside from one odd behavior: when the computer is entirely off, I cannot power the computer back on unless I attach the MagSafe adapter. Once the computer is on I can disconnect the power and it runs fine. It even displays the battery percentage in the OS. Taking the computer apart, I noticed that the board that is part of the battery seems to have been soaked with coffee.
So my question is this: Given the behavior, does anyone here have a guess as to whether it might be more likely to be the logic board or the battery?
I can purchase a new battery and return it if I don't need it (for a refund, less return shipping and a 20% restocking fee), or I can go for a $200 repair service that may just tell me I need a new battery. I'm leaning toward trying the battery first...
Is this a good question?