The first thing I would do is to try and solve the digitizer issue. It clearly doesn't work and it's certainly plausible that it coud be affecting other functions. While you're at it, take a good look at the digitizer connector as it is easily damaged (missing pins). While you're at it, take a close look at the surrounding components as you may have accidentally dislodged something.
If you have a known-good digitizer, that would be ideal. Once that is confirmed as working with your iPad, then you can attack the other issues, if they persist.
You really should disconnect the battery before removing the LCD. It's a numbers game but eventually you will blow a backlight circuit :>).