This problem is inherent in all EPSON DuraBrite printers (such as your model). The problem seems to be in the manufacturing of their vacuum tube assembly. The print head cleaning area of the EPSON DuraBrite lineup has a sponge for cleaning the print head. This sponge sits on top of a vacuum tube assembly which (suppossedly) pulls any ink clogs out of the print head into a dried-ink reservoir lower in the printer (near the pump that is connected to the vacuum tube). Or, in the case of the installation of new ink cartridges (per your case), primes the ink cartridge and pulls the new ink into the print head assembly.
The problem is that Epson manufactures their DuraBrite printers very cheaply, and the seal on the vacuum tube is VERY bad. The result is that (conveniently) just out of the warranty time period, the tube's seal fails and pulls away from the sponge assembly.
In short, the reason why your printer no longer works is because that seal has failed, so there is no vacuum pressure to prime (or clean) your new ink cartridges. The only solution is to buy a new printer or attempt to manually re-seal the vacuum tube assembly.
This webpage may give you a better idea of what's going on and how you might fix it. If you do a simple Google search for "Epson vacuum tube solution" or something similar, you may find more detailed instructions.