It sounds like it could be the power supply. that would make sense. If you take the cover off then you can get a voltage tester and see if the power coming from the outlet is getting through the power supply...BUT BE CAREFUL...electricity is very dangerous so do not touch anything with it plugged in. Unplug printer, take covers off, be careful not to tough electronic boards as they can still retain power. Plug it back in then only tough it with voltage meter ends. DO not tough anything with your hands. Only do this if you feel comfortable doing it. take some pictures inside and post them so we can see close ups of the electrical boards. Look for burnt or blackened areas as those would be your problem. Also solder connections that have simply come apart. Below is some links to places to get parts.
This comes from OLDTURKEY03!!!! Thanks!
For the printhead, contact this seller -
http://www.alibaba.com/product-detail/Original-new-Printer-head-for-Epson_377873939.html
or you might check on here-
http://www.worldclassink.com/Epson-Stylus-Photo-1400-Printhead-printer19580-ift18.html
the power supply board is part number 2093972 and is available right here
http://www.partsimple.com/2093972-eps-n-13.html
and special order from here
https://www.partstore.com/Part/Seiko/Epson/StylusPhoto1400/Seiko/Epson/2093972/New.aspx
Hope this helps, good luck.