When peeling back the tape in various steps, it's quite easy to tear it and the replacement motherboard I had didn't come with any new tape. I used electrical tape to secure the cables and components as they were originally and it seemed to work fine.
Additionally, since my broken unit had been unused for a while, the battery was totally dead. It took a while for it to show signs of life (left it plugged in for 30+ minutes) and I found that holding the power button and pressing the volume down button together for a few minutes also helped to bring it back into action.