The first thing is to always check the two feed/separation rollers in tray 2 for wear (part # RF5-1885).

One feed roller is in the cassette tray and the other is right above it in the printer cavity.

The next thing would be to check the paper in the tray. Sometimes when users add paper the bottom sheet curls up between the paper and the front of the machine causing the remaining paper in the tray to not lift properly as the paper supply is removed. If the paper seems fine then turn the machine around and remove the dust cover if it has one. This allows us, with a flashlight, to watch the pick up assembly as it goes through its process. If while watching you notice that the paper feeds up an inch or two then moves back a half-inch before feeding into the machine all the way we know we probably have a problem with the black torque limiter in the cassette tray. You can replace the limiter (part# RB1-8974)

with a new one or pull it apart and remove a little of the metal filings inside the limiter. Don't remove all the filings. Reinstall and watch again from the back. The paper should be moving correctly.

Additionally, watch the four half-moon pick up rollers (part# for the 4100 RB1-8957) (part# for the 4000 RB1-8865)

and make sure they are only moving when needed and getting back to the home position. There is a spring on the left side of the pick up roller shaft

that pulls the pick up shaft to make sure the half-moon rollers are facing up when the machine is not functioning. If you notice that the feed rollers are facing down at a ready state, make sure the spring is attached.

On the right side is the drive coupler, which is shaped like a black plastic dumbbell (part# RB1-8877).

Make sure its in place and not cracked. When this HP printer model was first introduced I was replacing two or three of these a week until HP made some changes to the paper tray to limit the amount of paper that could be installed.

The last thing to do would be replace the pick up assembly

Tray 2, 250 sheet (part# RG5-2672); Tray 3, 250 sheet (part# RG5-2684); Tray 3, 500 sheet (part# RG5-2672); Tray 2 for the 4100 (part# RG5-5277). I just replaced one the other day that was jamming every 100 to 200 pages to find it had a broken tooth on one of the drive gear arms.