HP PSC 1610 - multiple lines in scans and copies, prints OK

I have a 2 year old HR PSC 1610 all in one that has just developed a problem with scans and copies. The printer prints OK. When I scan or copy, I get a very precise, thick set of lines right in the middle of the page, over the image of what is being copied or scanned. I've cleaned the glass, I've done cartridge cleanings and alignments, I've restored factory settings and nothing helps. Is there some kind of scan calibration I can do, or will I need to take the thing apart to clean it? It seems like something with the actual scan mechanism that's broken.