Paper Separator Blade
I had an HP Laserjet that also used to jam. Problem was the paper separator blade which only allows one piece of paper to feed at a time. This is NOT something you can fix yourself - you need to take the machine back to HP (who will charge you a fixed service fee - which is about 40 - 50% of the cost of replacing the machine!) or to an independent servicing organisation who can access HP spare parts. I went the latter route and the machine carried on for another couple of years when I donated it to older son and heir who still uses it from time to time.
Good Luck!