Why is my phone turning off when I connect the battery connector?

The left side of the connector is the positive battery terminal (from the videos perspective), that’s probably why the phone lights up. If it will not turn on when the battery is fully connected, it’s either a battery issue (unlikely in this case) or a logic board issue. You may have damaged something when you did the repair. One thing you could try is to disconnect the Front Camera flex and then reconnect the battery fully to see if it boots up properly. If it does, then the FCAM flex may be damaged. If it doesn’t, then try disconnecting the entire screen assembly and boot. You’ll need to connect it to an iTunes enabled computer to see if the phone is recognized.