Sounds like it's time for a new printer.
What is "new" ink? How old is the so-called new ink you had laying around? Check the expiration date and if need be try a brand new cart.
As for the foam (ink pads) they have to be replaced, depending on your model some Epsons like my R220 you can "mod" so the ink runs out the back and avoids the pads altogether. Unfortunatly it's like a jigsaw puzzzle trying to open them and replace little pads...Epson reccomends you buy a new printer.
If you google around and find a way to mod your Epson, you still need to reset the "end of life" in the FW. you can get the software now from Epson.