Water damage : logic board?

Hi everyone,

I have a Macbook 2010 unibody that suffered water damage in 2011. At that point, I took it to a shop, and they cleaned up the computer but told me it was a loss (though they managed to backup my hard drive). I left the computer in a closet for 4 years and last year decided to try turning it on before selling it for parts. The computer turned on fine but some keys were not working (the initial damage happened through the keyboard). After that one time, it never turned on again--even after charging it. I opened the computer and don't see any signs of corrosion, though I haven't taken it apart. Does anyone know what that might indicate? Is it a battery issue? Is it safe to assume that, since the laptop started fine once, the logic board is okay? I'm trying to decide whether to sell the computer for parts or try to fix it myself, so I'd appreciate any help or advice. Thank you!