Most likely the lcd has gone bad, but to be honest the iPad 2nd generations are getting pretty old and slow. It may just be best to get a new one or a newer used one.
Its simple, you need the screen replaced again. If you were recently in a shop to get it replaced they may give you a little bit of a deal. I usually do for my customers depending on how long ago they had it repaired. But depending on what the inside looks like when they get it open they may tell you to get a new phone. Depending on the water damage. I would advise against using a smart phone in the shower.
You would take the main board out of the tablet with the broken screen and put it into the one with the working screen. That would be the easiest thing to do. If you do that you will be good to go!
Are you out of storage space? Its possible that the version of android you are running is becoming to outdated. It looks like the most current version you can get for that device is 4.2.2 .
Will it start with starting fluid? I would take the spark plug out and see if your getting a spark. If it still wont start. The cylinder wall or piston rings mite be damaged causing very low compression.
In my experience its usually a bad battery. Its possible that the charge port could be bad but most likely the battery just needs to be replaced. Both are pretty easy to replace. Or pretty inexpensive if you have to take it to a shop.