Overheated & now won't turn on after LCD/digitizer replaced

I was given an iPhone 4 by a friend who lost it in the snow. He found the phone after apparently a car drove over it, since both the back and front (screen) were badly smashed. Oddly enough, the phone was working fine, everything, even the digitizer.

Now, I replaced the screen, but when I tried turning it on, it turned on, showed the screen working fine, launced some apps, but in a couple of minutes it was overheating pretty bad in the rear camera region. Turned it off, disconnected the battery, let it cool, took a little bit of it appart again to make sure that everything is connected right, put it back together, and without turning it on, as soon as I connect the battery it starts overheating. After that it's not even doing that. Connect the battery, nothing, no heat, no power. What can it be? I'm pretty sure it didn't get water damage from the snow, since it worked perfectly fine for about a week after the incident, until I replaced the LCD. Any ideas?