The only things I can think of which may help would be to clean out the machine completely. Toner dust and small particles can set off paper jam sensors. I would take alcohol & water and clean off every rubber wheel that moves the paper through the machine. Then inspect them one by one for wear. If you have a wheel with a flat side it won't handle paper correctly and the delay in timing will set off paper jams. Over time the rubber on the wheels gets sticky or dull and does not pick up the paper correctly. The software installed on the pc's times the paper processing procedure and when things are not in tuned it will think there must be a paper jam.
The other thing would be to reset the machine & update the software in all pc's that use it as a printer before reconnecting it again.
The reset the machine, disconnect any cables to pc's using it and then turn it off and unplug it from the wall. Press and hold the power button with the power cord disconnected for sixty seconds or so. Then go to each pc that uses it and uninstall the software for the HP. Then go to HP's website (
www.hp.com) and download then install the newest version of the software on each computer.
Another thing that causes paper jam sensors to go off is using the wrong kind of copy paper in the machine. If the paper is too light the feeders will throw it through the machine too quick. If its got a smooth texture to it the paper will not be picked up as it it supposed to.
If I were you I would go to the local stationers and purchase a good grade, heavy weight copy paper to use on the machine to rule out that the type of paper being used could be causing the trouble. It may be expensive, but buy a single rheem of really good paper thats made for copiers and remove all of your old paper and reload with the new before reconnecting all pc's again.
After the new paper is loaded and the machine has been cleaned and inspected, and all pc's have the newest version of software installed on them plug the machine into the power source again and run a few test sheets.
If you still get the same problem after all of the above, then I would say its some sort of electrical sensor problem that needs a tech on site to figure out and repair.
Good luck! And let me know if any of the above helps to solve the problem.