Unfortunately, all of the issues were still present, nothing had been fixed. After putting everything back together, I hit the power button and nothing happened, so then I plugged it in and it powered on (on its own, no power button press). My latest attempt was to purchase a new MagSafe DC-In board (820-2565-A), which I installed last night following a Youtube tutorial. New cable still just showed green light (even with new battery), and when I unplugged the cable the computer would shut down, X symbol still on the battery icon. Then, I bought a new charging cable (old one was in pretty bad shape, so I was hopeful), and tried that out, and once again nothing changed. After installing the new battery absolutely nothing changed (same battery X symbol, shutdown whenever unplugged, charger only showed green light). Moving onto hardware, I first started by buying a new battery and replacing it. Either way, I definitely reset the SMC later on when disconnecting and reconnecting the battery, and that did not fix the issue. For the SMC reset, it was difficult to tell whether or not it actually reset the SMC, because after holding the keys for the required time and booting the computer, nothing was out of the ordinary, but I'm not sure if there should be something different that happens that lets you know the SMC was successfully reset or not. For the NVRAM I'm pretty sure it worked properly because it repeatedly rebooted until I let go of the keys, but still the problem wasn't fixed. The first thing I tried (after doing some research) was to reset both the NVRAM and the SMC.

Whenever I unplugged the charging cable, the computer would shut down soon after, indicating that it wasn't able to power the computer without being plugged in. A couple of weeks ago, my 13” MacBook Pro (Late 2011) started to display a X symbol on the battery icon, and the light on my charging cable would only show up as Green (never orange).

Macbook pro battery x symbol