Chosen Solution

I recently bought a non-functioning iPad from my buddy. I knew it needed a new screen, so I replaced it. But I made a mistake. When i first attempted the repair, i used my plastic opening tool to pry up slightly on the socket, thinking it was held in place similarly to the cables on an iPhone5s. I damaged one of the connectors a bit. Is there a way to fix this? If necessary, would I be able to buy a new digitizer connector and replace the one on the ipad?

Yes, you can replace the connector with a new one, it is soldered onto the logic board. On the schematic it usually says the type of connector it will be. Personally though, it will probably be easier to buy a logic board and just swap it, since they do not go for a lot now.