Battery drain and gmail

[mhdroid90]

So I've had this phone for about a year, and no problems until yesterday. First it started shutting off by itself, when I turned it back on the battery was nearly dead. I didn't do anything to it, except put it on a charger. I left it alone for around an hour, came back, and it had turned off again. I started it again and the battery was lower than before I had started charging it. Then it shut off and I started it several time, sometimes the screen wouldn't unlock and it seemed unable to load my home screens. I managed to uninstall any apps I had downloaded in the past week, and that didn't help anything. I restarted and did a soft reset. Still not working, so I did a hard reset. It's working now and I haven't installed anything on it. I tried to sign in to my gmail account that I've been using for the phone and it kept saying I had an invalid password, I went to gmail through my computer and had an email that said someone had tried to log into my account so I reset my password. I tried to sign into my gmail again and the phone shut off. I tried signing in with a different account that is linked to my main gmail, and it worked fine. How do I go about getting my gmail to stop shutting the phone down? Or what else could be happening. Also, it killed my battery. Was at 80%, down to 10% after I tried to sign into the main gmail account.
I tried to load the other gmail and it shut off again. ugh

TL;DR - My gmail and phone are refusing to play nice, how can I fix this?