Check that other electronic devices connected to same power socket have power and try another mains socket and another power cable if necessary. Failing this try another suitable and known-working power cable. Depending on your scanner, a standard "kettle lead" or "figure of eight" power cable is used. If there is power to the scanner (indicated by an illuminated Start light), when a different power cable is used, then the fault is with the original power cable.
If the unit does not power on after following the checks above, contact Epson for support. If your scanner uses an AC adaptor, then this may need to be replaced. If your scanner is over 12 months old, you can purchase a replacement AC adaptor directly from Epson.