If your ipad has a dented corner, you may need to trim the new glass a bit so that it fits flush. The ipad I worked on had been dented in the corner, which what cracked the screen in the first place. The dent pushed in the metal lip enough that a replacement screen would sit on top of it, so that a little too much pressure on the glass will make it crack again. A diamond-coated file will work to file off some of the glass on the corner. Full sized Leatherman multi-tools often have a diamond coating on the back side of the coarse file — it works great. Just be patient as it takes a while to grind off.
Good tip! I replaced a digitizer myself after a shop had done it once already. Aside from new cracks, there were problems with dead spots on the screen, and the lock button would shut down but not sleep the screen. The screen I took off looked like the digitizer cable had been pinched like you noted, and I wonder if that was causing the problems.
The one thing missing here is the new battery, which from Sony costs more than a new player! The closest fit to the size and capacity that I could find came from www.batteryspace.com product number PL-544792-1C
I paid $8.50 each plus shipping for a total of about $23.
Carefully pull the coverings off the original pack and remove the tape over the connections. The wires to the tabs should come off with enough heating from a soldering iron. Those wires can then be soldered to the tabs of the new cells. Then cover up the connections with electrical tape and wrap the covering around the new cells. It fit back in the case perfectly, and works great. I'm just passably handy with a soldering iron, so it took me a good 60-90 minutes to carefully take the battery pack apart, resolder, and reassemble.