The overheating problem is most likely damage to a power IC. You stated you damaged one of the connectors going to the home button. It also sounds like you damaged a power IC or the battery connector, which overheating is a classic symptom of.
Pull the screen and the battery. Check out the battery connector on the motherboard and inspect for damage. Did you bend or break any of the pins? Also check the ICs located near the battery connector. See if you can see any that are damaged or an area where one is missing.
This one is usually a pretty easy fix but it does require soldering skills.