-It's probably safe to assume that the battery cable has been fully inserted while I've been using it. Besides today, since I got it serviced ~2 months ago I haven't opened the back cover. Also, the issue happened much less for a little while after I got my laptop back. It's just become more frequent in the last few weeks.
-I did notice that the random cuts occur more often after I open a game and temps start to rise. Not sure if that's enough to cause the burns.
-I read some of the other threads about random shutdowns. Some people are saying its BIOS related, but even when I was on an older BIOS, I still had the sudden shutdowns/power cuts. Also, my battery hasn't been detected by the OS since I posted the OP. I've just had my laptop connected to AC.
Seems like the next step for me is to call to get my battery replaced :l.