I had the same problem some time ago with a Dell printer - I can't remember its model number, but 944 rings a bell.
Like yours, I got a 'Clear Jam' report, and nothing I could do would get rid of it. And I mean nothing! I tried opening up as much of the printer as I could, to try and find some rogue scrap of paper, I left it unplugged from the mains for a while, I tried it on a different computer (driver software and all), and so on.
Eventually I'm ashamed to say I dumped it. I always hated it - build quality was mediocre, the paper feed was vicious and unreliable, the scan quality was poor, and to be honest I wasn't sorry to see the back of it. Today I reckon you can get something of better quality for much less money.
Sorry if that's not very helpful!