This sounds like several challenges occurred during your repair. So, let's see if I can help. The first issue that you're describe makes it sound as though the digitizer cable is broken. If that is the case, it not only will prevent you from using the touch screen, but may cause an electrical issue with the logic board. It also sounds as though several other cables and connectors may have been damaged durin the tear down. As you know, Apple uses very fine solder connections to attach these connectors to the LB and even a small amount of torque can break a connection.
You list so many issues that I'm not sure where to start. Do you have access to an iPad schematic? If so, my first recommendation would be to start checking voltages from the battery forward. To resolve/check each of your issues will require an isolation-check plan.
Best of luck!