Your phone has water in side is at risk of zapping at any stage- stop using it! it needs to be dried out ASAP before you should attempt switching it on again, the only way to properly do this quickly is to have the phone opened up .
Make sure the circuit board is seated and screws are tightened correctly. below the circuit board are cooling pads if your main board is not seated in the phone correctly this can cause overheating. Also your cameras are not operating check to make sure they are plugged in correctly this could be causing short circuit and potentially overheating
The reason the iPhone batteries are held down with the silicone original tape is for heat transfer in an attempt to prevent battery from overheating , using correct will prolong battery life
I have had this problem before it turned out to be the touch ic and a crack in logic board . if you pressed down on the logic board it would work fine, it's possible when the screen was replaced with your test by the repair guy simply pressing in plugs that fix it temporarily and not new screen. Try pressing on logic board see if this fixes if not replace screen. The 6+ often have bad or broken connection on circuits to ic's caused by bending and flexing ontop of corrosion issues that leads to touch disease.
The 2-step is sending a SMS message can you put the SIM card from your disassembled phone into a working phone so you can then receive this SMS with 2-step code?
