Same kind of problem with an old HP LaserJet 1300 we still use. It began by it occasionally picking up multiple sheets of paper and jamming. It gradually got worse until the printer wasn't usable anymore.
The issue turned out to be the solenoid for the pick-up mechanism. When activated it should cause the pick-up mechanism to turn once. The solenoid once apparently had a small rubber pad to reduce noise. This had turned into goo and the solenoid would stick causing the mechanism to turn multiple times.
Fixed by removing the left-over goo and a piece of tape. Ten minute fix.
The issue turned out to be the solenoid for the pick-up mechanism. When activated it should cause the pick-up mechanism to turn once. The solenoid once apparently had a small rubber pad to reduce noise. This had turned into goo and the solenoid would stick causing the mechanism to turn multiple times.
Fixed by removing the left-over goo and a piece of tape. Ten minute fix.