Replaced battery, doesn't charge or work without power adapter?

Hello there! I recently purchased a 13" 2007 Macbook (Black) A1181 as a small project to keep myself busy, and to use as a music-making machine on my free time. The machine runs great, with an upgraded 500GB HDD and a 4GB RAM. It's currently running OS X 10.6.8 (Snow Leopard), but I plan on upgrading it to Lion and, if possible, from there, Yosemite. The machine works well. The only issue I have with it is that the battery it came with was defective, so I replaced it and bought one for around $15 on eBay. Upon arrival, I plugged it in and it showed up, but would not charge. A few days (2 or 3) after I installed the new battery, "No batteries available" is showing up now and I can't get it to work on the battery, only when connected to the power adapter. Please bear in mind that this was an issue already, as the battery it came with was defective (it being 8 years old, I think it's justifiable). I'm confused and want to know if this has anything to do with the MagSafe connector, or the battery connecter. I'm willing to have any of this replaced and get this machine working. Any advice?