"so I had to pull them through the rest of the way with a little force
Don't do that next time, ALWAYS remove the screws instead of forcing !
You would loose maybe 10mins but now you lost 200$ !
"Is it possible that the cables got damaged in doing this"
Yes, of course, this should have been done carefully.
"If so, does that mean I have to buy a screen/digitizer replacement"
First check whether the cables are damaged or not, and check if you can repair them easily or if you have to buy new.
Last, check if this is the problem, it sometimes happen we trust something is faulty but finally it's not.