'No batteries available' warning with new battery??

I have a 2006 Macbook with a 2 GHz intel core.

Recently, my macbook's battery needed to be replaced due to years of being plugged in constantly. I bought a new battery for it and when I put it in, the battery icon in the top right corner of my screen has an X through it and says "No Batteries Available". I thought I'd found a solution through another forum, which told me to drain my battery and recharge a couple times to get it to work. I drained the battery and then figured out that the new battery doesn't charge when the power adapter is plugged in. I can put my old battery back in and it goes back to the way it was before, charging and showing how much life was left.

I have absolutely no idea as to why it's doing this and every other forum is discussing newer Macbook Pros so they don't help me at all. I don't think this has anything to do with the battery problems that Macbooks as old as mine are having, such as swelling or stopping unexpectedly one day.