I just posted a question almost identical to yours here, but I have figured out what is wrong with my 6500 Wireless, I just don't know how to fix it.
If your printer is like mine, what happens is when you put paper in it there is a little white plastic roller that just checks the height of the paper stack. On mine is it on the left side and can be seen by looking in to where the paper is stored in the stack waiting for printing. However, there is a second mechanism that is needed to make the printer load the paper to the main rollers where it proceeds with printing. Try printing something while you are looking into the stack of paper and see that little white roller. If a second small set of rollers descends on the paper and feeds it into the main roller apparatus I am not sure what your problem may be. However, on mine, that set of 3 rollers never descends and feeds the paper to the main roller assembly, so that assembly says, "Hey, no paper!". I don't know if there is any way to fix this problem. I am waiting for my answer and I am fully ready to take my printer completely apart if I can fix it.
If your printer is under warranty I would certainly make it HP's problem. It is my opinion that if you take it someplace to get it fixed it could cost have the price of a new printer at least.
I needed to print/scan/fax in a hurry so I bought a replacement (another HP, as I have had good luck with them over the years). But am trying to fix this one as a spare.
Good luck and see if this is your problem. Also, the printer mechanisms may differ between models. If yours does not work this way, just disregard all this.
Bill.