Not sure what's wrong anymore

Hello, I think I'll start off by saying I'm new here and I'm a complete idiot when it comes to computers so sorry if this is both a simple/obvious fix and in the wrong part of the forum.

Okay so, a while back my laptop, a two year old Sony Vaio with Windows 7, started just popping off. Like, the screen would turn black accompanied by a "pop" noise and turn itself off. I could easily turn it back on and a screen saying "Windows did not shut down correctly" would appear along with the options to start up normally, in safe mode, etc. And then I'd notice the laptop would be really hot, so I assumed it was just overheating.

I figured I'd clean the fans then buy myself a cooling pad to help me in the long run of things. The pad has helped, haven't had it pop off since I bought it a week ago, until now. I didnt have the pad plugged in as I just wanted to check my emails before work, but before my computer could even connect to the wifi (which has been taking longer than normal) it popped off, barely enough time for it to even get hot as it was only on for a minute. I waited a bit, put the pad on and started to go about my business when 30 minutes later, even with the pad on, it popped off again.

Now, is my computer overheating or is this some other problem entirely? Sometimes my battery doesn't take the charge when I have it plugged into the charger, I have to fiddle with the plug to get it to take. Could it be a problem with the battery?

Thank you!