Unresponsive screen after Apple Care repair.

Hello,

I recently dropped my iPhone X and the screen cracked, as well as the digitizer becoming unresponsive to touch. Since I have Apple Care (I’d usually repair it on my own) I decided to go through them and get the screen replaced. After the replacement today the screen is still unresponsive - they were going to replace the unit for $100 (and still will) but I told them I’m just going to pay the $30 for the replacement screen and take it as is because I don’t want to lose my data (I was stupid enough not to back it up) - has a ton of memories with my family, friends, and a ton of content I cannot lose (or refuse to lose).

My question is - I have a new screen now. It’s unresponsive. But I know it’s not the screen because they tested everything at the store. The guy said it’s on the logical board, or it’s what the screen connects to (same thing rather I guess) so my question is, how can I replace this, what part do I need to replace what the screen connects to? Is the memory connected to the logical board? Just bummed. Hoping someone has answers.

Also, maybe someone knows how I can back up the phone in its current state? I can’t unlock it (face ID is disabled now with the new screen replacement until I get back in) so I don’t know what I can do at this point. The USB accessories stuff also won’t work until I unlock the phone either. So.. what can I do? I’m at the point I’d pay for it to be repaired so I don’t lose all my data.