Way to tell if battery needs replacement after water spill?

A small amount of water was spilled on the keyboard of my Macbook Pro about a week and a half ago. I immediately turned it off and cleaned up what I could.

Not thinking very smartly, I left it right side up for the night, when I opened it the next morning there was some water condensation on the screen in the shape of the keyboard. It turned on, but only a few keys on the keyboard were working properly, so i turned it back off and put it upside down again. I knew this was bad so I left it upside down for a day then removed the back case when I could and let it air out more. There wasn't any obvious damage but it would not power on now and when I plugged in the charger a VERY faint green light only showed.

I needed my data, and am lucky enough to have another Mid-2010 MBP not being used anymore, so I put my hard drive in there and it worked like a charm.

Now, about a week later, when I got the screwdrivers needed, I read some guides online and took it apart and removed the battery and logic board and throughly cleaned the logic board with isopropyl alcohol, even though there still wasn't too much obvious damage or corrosion. I applied new thermal paste, and put it back together, and it still didn't turn on. I tried putting the battery from the working MBP in the damaged one and it turned on! But the keyboard was still acting strange.

Time for my actual question: does this most likely mean that my battery is shot and I should just replace it, and do the same for the keyboard? What should my next troubleshooting steps be.

I'm somewhat knew to DIY laptop repairs, but am pretty technically inclined, and want to learn so I won't mind doing the keyboard replacing myself.

Thanks for your help in advance!