Officejet 4620 Not printing, not pulling paper through

I have always had sporadic issues with this printer; nothing serious usually, mostly it claiming it was out of paper when it wasn't. Today it decided it was done with me. I loaded in new paper and attempted to print something. At first it said it was out of paper, then it would pull a piece of paper up into the printer about an inch, stop, and claim there was a paper jam. The paper was peeking through the rollers just enough so that I could pull the new, unwrinkled sheet of paper out and try again, to no avail. I have reset the printer several times, cleaned the rollers, updated drivers, reinstalled the software; nothing works. If anyone has any advice, I will be most grateful.
Thanks.