The printer draws ink through to the waste pads in the bottom of the machine. There is a silicon tube that runs from the pump cap to the pads. This tube can get clogged with dry ink if stood for a while or if you use rubbish compatible cartridges which do not contain the anti coagulant (spelin iz not my strong poynt) used by Epson.
Get a service manual from www.TheServiceManualShop.com and use it to remove the covers to get access to the tubes. If they are clogged clean them out in water and reassemble.
Clogging will also render any number of head cleans usless as the head clean uses vacuum from the pump cap to suck ink through the head. If ink can't pass through the tubes, no vacuum can form
Mike Burton
September 2006