Reversed jumper cables...ugh!

I have my 2008 Limited in a body shop and I when I went to pick it up the battery was dead. They brought out a booster pack but it wouldn't even click. After a few tries I got out of the car and saw that the guy had the cables on backwards. I told him to switch them and it fired right up. I went to open the hatch and it wouldn't open, either with the key or the remote. I cycled the locks with the remote and I could hear all the door locks clicking. They went down to the auto parts store and got a new battery, thinking that the old battery was the issue. No luck. I started checking different components and found that the tail lights, turn signals, and brake lights also didn't work. They checked the fuse box that is inside the car under the steering wheel and they said that none of the fuses had power. There's a fuse marked IGN in that box, and I would think that the car wouldn't start if there was no power at that location. My questions are these:
1. Would it start if there was no power at that box?
2. Would the dead battery cause the tailgate ECU to malfunction?
3. What components might have been damaged by reversing the jumper cables? (I want to check everything that might be damaged before signing off on it in case they fried stuff on my car)
A few more details for diagnostic purposes: the tailgate was repaired, so they removed everything from the tailgate so they could paint it. I opened the tailgate one time and shut it before the reversed jumper cables. Also, when they tried to hook up an OBD reader to it they couldn't connect.

Any insight is much appreciated!

 

Ouch!! Good luck to you tracking that one down. Too bad these outfits don't have a reset switch like the computers that they are.

 

If it’s a booster pack it typically has polarity protection, and in fact did nothing.

otherwise check every fuse related to the systems you have issues with.