Note that there is a difference between a paper jam and a carriage jam, although one can cause the other. Auyeung1962's answer worked for clearing a carriage jam message on my HP PhotoSmart c4385 that persisted after the paper path was clear, the print carriage was moving freely, power was confirmed, and a hard reset had been performed.

Specifically, the carriage Auyeung1962 refers to is an inkjet wiper tray that sits under the cartridges on the right side of the printer. The tray should slide easily back and forth, at right angles to the print carriage, with just a little hesitation when the wipers go under a scraper bar that sits behind the carriage.

My c4385 was out of warranty and had printed almost 9000 pages when enough ink had accumulated to gum up the wiper tray rails. I cleaned mine with cotton balls, a hemostat, and cheap vodka. I don't think it took me so long, but I didn't go nuts, just cleared where the moving parts slide. I was careful not to get alcohol anywhere where ink doesn't normally splash.

When you've got the tray moving smoothly, make sure you remove any stray cotton fluff, especially from the rubber wipers. Then close up the printer and print a test page (On the c4385 press the Cancel and Green buttons).