It sounds like it's more than a paper jam. Presumably you have cleared the paper path, anyway. Are inkjet cartridges full or is one empty/dried out.
I generally warn friends against buying combine scan/print units and against inkjets, many of which have poor reliability and high running cost.
Even if it's out of warranty I would return it to the dealer -- you should be able to expect reliable service from a consumer durable like this for well after the warranty expires. The only way manufacturers will learn is if the dealers end up paying for repairs and refuse to stock an unreliable brand.
If that's not successful, hopefully some of the HP unit's functions are still working.
I would consider a standalone printer (preferably laser).