Dropped in water, cuts on, screen unresponsive to touch

Jane, you will have to take it completely apart. Since it got submerged, it needs a proper cleaning, otherwise it will for sure die of corrosion damage later on. Disassemble it, and clean every part with a high grade isopropyl alcohol, 90%+ preferably. Use a soft brush to clean every nook and cranny of the board, do not forget the connectors and cable ends. Check for any missing or charred looking parts. Take your time with the visual inspection. After that, replace the battery, this is to prevent failure later on. Reassemble your iPad and see what you got. Best case scenario is a broken digitizer, worst case is a shortened digitizer IC and other SMD component. Hope this helps, good luck.