Do you have another fax machine to try to connect to the line? not that this step is vitally necessary, nor probably informative as to what's wrong.
I suspect at this point that there's nothing to be done (except the above test, to be quite certain of the diagnosis) except to assume that your fax machine's electronics are 'broken'.
Unless the following clears up the problem (for I am not certain that you have tried power-down resetting your machine yet):
Turn the printer OFF, when it is on, by suddenly and sharply unplugging it from the power source.
Also unplug it from the computer!
Leave it that way for 10 minutes.
Plug it back in to the power only, not the computer.
Turn it on if it didn't turn itself on. Wait for it to initialize.
Try whether it works now, as a fax, by also connecting it to the phone line (but not the computer, yet).
Additionally: you might want to check the setting at the bottom of this help page, the one about Dial Tone Detection - if it's On, you might want to try setting it to Off. It can't hurt and certainly is worth trying:http://files.support.epson.com/htmldocs/art810/art810ug/wwhelp/wwhimpl/common/html/wwhelp.htm?context=Epson&file=fax.6.9.html