Macbook Pro: Battery Replacement or SMC reset?

I have a 2011 MacBook Pro that has been acting odd since March. In March, I was on my computer one night and it suddenly shut down on me. I tried everything to turn it back on, but ended up taking it to the Apple Store for repair. On my AppleCare service repair summary, it said they replaced my logic board, did some kind of repair to my RAM, and replaced my Magsafe board. It was working perfectly fine until about the middle of May. It shut down on me randomly a couple times, but once I plugged in my charger and waited a few seconds, it would come back on. More recently, I'll plug in my charger and if it accidentally gets unplugged, my laptop will shut down on me again. Every now and then, the battery indicator lights on the side will also blink (which I know means replace the battery). I've also noticed that my fan will run a lot more than it used to. It gets overheated, specifically when I'm streaming Netflix online. Regardless, every time I shut down my MacBook Pro and turn it on, it reboots with the white Apple page and a little progress bar. It usually takes around 30 seconds for it to reboot.

I know this is a little specific, but I'm not sure if it's maybe just my battery, or if I should reset the SMC. I would consider taking it into Apple again, but not if I'm going to have to pay another hefty amount for something that I could do on my own.

Thanks for your time!