Bulging Battery, Now no power

So I received a Macbook Pro 15" Early 2011 Model A1286 laptop. I noticed right away the battery had swollen enough the trackpad was popping out a little bit. I was told they had been using it like that for a while then it simply stopped working. Now my first thought is they ran it into the ground and the bulging battery fried some important components on the logic board. So I took out the battery and tested the laptop with just a charger to test and I didn't get any indicator lights.

So my question is, is there any good way to test the logic board to see if there is any power to it at all or if maybe a single component went bad? I'm not against calling this one dead, but I always like to do as much as I can before I call the time of death.