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Power failures can damage electronic equipment owing to associated surges and 'spikes'. A power surge protector for every electronic device of any value is an investment that always pays off in the long run.
Do you have any other telephoning device on the line with the fax? if so, unplug it from the line, and try just using the fax by itself, see if it goes through. (If not, likely your Epson's fax facility has been damaged by power surges during the original power failure, I'm sorry to say.)
Note: if you have VoIP or digital phone service, your digital phone service may be disabled or 'broken' or damaged, instead of your Epson fax. And if you don't have digital phone service, try contacting your phone co., tell them that you are having trouble faxing since a power failure, and ask them to do a line check for you. This is a routine measure, I don't think they will even charge you (since the report allows them to make sure of their phone transmission network condition in a critical place and improve their service quality etc.)