Hi akwardllama1234,
Unfortunately, you need to (at the very least) open your phone up again. Disconnect the battery first, then disconnect the screen. Clean the connectors with >99% isopropyl alcohol before reconnecting in reverse order. Test to see if touch functionality is restored before closing up the phone.
If the clean and reseat doesn’t fix it, you’re looking at a screen swap, to be able to get touch working so you can recover the data. There is no way to get the phone connected to a computer and authorizes for backup, without touch functionality.
The 6 / 6 Plus phones had something called “touch disease”. This was because the touch IC on the logic board failed. Not applicable to 6S and above, because the IC is no longer into logic board.