The things to check to verify the above suggestions for repair would be your coolant level. Check it when the vehicle is cold and see if it is lower then it should be and if it is getting lower. Also pull the oil fill cap and look on the inside of the cap, is there any milky buildup? If so you are getting coolant in your oil.
To me this sounds like a grounding issue not allowing the battery to charge completely. I would recheck and make sure I put back all the brackets and ground straps in their proper place and orientation.
This could be a few different things. The first being a battery. Depending on the computer it will not run off plugged power but only power from the battery, so if now power is going through the battery it won't come on. The second could be a port issue where you plug it in, if its damaged power may not be going through it. The third thing I can think of would be a damaged solder joint in the computer where the power leads hook up.
I've seen it done with heat but you have to be careful and heat evenly. I have personally done glass removals with dry ice and some success. With this method you lay the screen on the ice till the glue freezes and turns loose. This can be tricky though because if you get it too cold or not cold enough you will damage the lcd when trying top remove.
Most likely this is being caused by the screen not sitting right in the mid frame. Loosen screws securing screen and make sure everything is aligned. When re-tightening do not apply pressure to either screen or mid frame. have the assembly resting on a hard surface and tighten the screws.
The case is a fixed piece on the hero series cameras. If it broke and its within a year gopro should replace it without much hesitation. Outside of that you will have to go back to gopro as there are no aftermarket cases for it.