Liquid Damage, erratic behavior on battery

I spilled beer on my air, it wouldn't turn on at all. I took it in to the apple store and was simply informed that it would cost $750 to repair, so I bought the tools and decided I'd try cleaning it myself.

I took the back off and battery out and cleaned a little, but didn't see much residue (there was a bit, but not on any visible PCB, only on the aluminium and battery. I cleaned it off the aluminium, mostly off the battery -- on the middle cell there are some... shiny patches on the bottom side that don't seem to come off.

I found out that if the battery is absent and the power plugged in, the computer can turn on and functions normally, if the battery is in, sometimes it works. If the battery is in but unplugged and is not screwed in, it works on AC power. If the battery is plugged in but not screwed in, the computer will start on AC power, but recognizes the battery and if the AC power is removed it will function on battery (I didn't try this for very long). It will not, however, power on with just battery in that state.

If the battery is connected and bottom plate are both screwed back on it doesn't seem to be able to power on at all, AC or otherwise.

So, what should I do? Would replacing the battery possibly help? Could there be damage elsewhere? Should I get a multimeter and test things, and if so, what should I test?

Thanks,

--Derek

e: other notes. When plugged in, the power adapter has a green light and also when able to start the computer with the battery plugged in, the battery reports full charge.

Also, based on answers to other liquid-damage-related questions, sounds like its a good idea to get a new battery regardless, so I'm going to do that (probably through apple since iFixit is out) but I would still appreciate any advice or insight into the problem.

e2: took it to apple store a second time, this time to get the battery replaced. They replaced it (for free!!!) and now it works perfectly.