What is the flash pattern?
If the red paper light and the red ink light are blinking in an alternating pattern, then you may have a foreign object or piece of paper blocking the movement of the print head. Turn off the printer, open the printer and look for anything in the printhead path. Remove anything that doesn't belong. Some printers have a strip that the print head travels across that can sometimes come out of position. This can be repositioned by moving it up and down as well as forward and back to align in a guide on the back of the print head.
After clearing the obstruction, close the printer and turn it back on. If the error persists, then the unit needs service.
If the red paper light and the red ink light are blinking together and the green power light is off, then the printer has an internal error. Turn it off and then back on. If the error persists, the unit needs service.
One internal error could be the waste ink absorber is full. These pads are below the printhead and absorb ink during cleaning cycles. To reach them is messy and takes disassembling the printer from the top. This may include removing the print head. Pull the pads, blot the ink off them and the places where they fit in the printer. Run clean water over the pads until the water remains clear. Dry the pads (use a hair dryer to speed the process). Then reassemble the printer.
Next navigate to http://www.epson.com/cgi-bin/Store/support/InkPadsForm.jsp
and fill in the model and serial number of the printer (as well as the other required information). You will get a link to download a reset utility for Windows. Run this tool to solve the error. Do not run this utility until the pads are replaced or cleaned; waste ink will get everywhere inside the printer and over your documents.
I hope this helps.