An A320 flight crew diverted to an enroute airport when their navigation system reverted to IRS NAV only and they were unable to program their route. A power interruption at the gate prior to departure may have initiated the anomaly.

Narrative

This event involved a loss of primary navigation mode (VOR; ILS) for both the Captain and First Officer. On the ground in ZZZ2 the power cord was removed prior to the APU running. On the Airbus this causes numerous electrical problems ECAMs; warnings and cautions. Once the electrical power was restored and the screens were normal (this took several minutes) we did a check of all the systems and all appeared normal. What we later learned was that apparently the NAV system defaulted to the standby navigation mode with only minimal indication and some abnormal indication it had done so. Once airborne and on climbout we received a NAV accuracy downgrade; followed shortly thereafter by an IRS NAV only message. We were unable to enter anything into the RAD/NAV page. After protracted troubleshooting with Dispatch and Maintenance Control we made the decision to divert to ZZZ in order to do a ground reset. ATC did declare us an emergency aircraft although we did not request it. ZZZ was chosen as the divert airport as the weather was clear there while it was IFR with CBs at our destination.