This is a common problem on Epson printers. I had it on an old 880 of mine. When the cartridges are in their 'at rest' position, the print heads rest on sponge (or felt) pads that soak up any excess ink. Over time, these become saturated, and the excess ink from the pad wets the cartridge print head. Then, when the print head moves over the paper it leaves a trail of black lines behind. Cleaning these pads is a real labour involving lots of damp kitchen paper towels, (depending on the model, you may not even be able to get to them!), and, there's no guarantee of success. Alas, having someone do the job for you would almost certainly work out more expensive than buying a new printer.