Why won't my MacBook operate with a new battery?

Hey guys, I have a question that I can't quite figure out through all the forums.

A few months back my MacBook battery had died. The laptop would run slower, but it was fine seeing that I rarely used it. The power adapter always showed a green light even thought the battery was inop.

So I recently purchased a new battery online and swapped out the old with the new today. With the new battery in, the computer won't boot properly and shuts off after a few seconds.

But with the old battery the MacBook will power on just fine (just operates slow) and will even run without the battery. But the second I plug in the new battery, it won't boot correctly, and immediately shuts off after a few seconds. I've tried several different resets like the SMC, and power manage my reset. If you guys could help a brother out, it would be greatly appreciated. I'm just wondering if it's a faulty battery or not. Thank you!