I bought a broken late 2008 13" Aluminum Unibody MacBook on eBay. Supposedly, according to the listing, Apple had said the original battery needed to be replaced. The other issue was the slightly-damaged battery cover. The computer arrived and, upon powering on, did not even detect a battery indicated by the [x] mark on the screen. Hitting the battery indicator button on the side of the case also indicated no battery. I assumed the battery was completely shot and I bought a replacement third-party battery. The computer doesn't detect this battery either. I've performed PRAM and SMC resets. I tried two different magsafe chargers to eliminate the possibility of a bad charger.
At one point, I was looking at the system report and the magsafe led suddenly changed to orange from green and the computer powered off suddenly before immediately turning to green.
I haven't removed the logic board but I have removed the bottom cover and I don't think this has any liquid damage. The computer works perfectly aside from the battery issue.
I notice the original battery seems to have terminals on the walls of the battery connector that the replacement battery does not. See photos below:
Note: this model is the late 2008 13" unibody, aluminum MacBook. This is NOT a MacBook Pro but actually the only aluminum MacBook ever made. It is very similar to the MacBook Pro but has subtle differences which should be noted.