Diagnosis
The internal fuse or circuit board protection may have been tripped by a power surge when the electricity flickered. It's a common failure mode for electronics.
How to Fix It
First, check the basics. Make sure the power cord is firmly plugged into both the wall outlet and the unit's socket (on the back, near the bottom). Try a different wall outlet that you know works. Check your home's circuit breaker or GFCI outlet to see if it tripped.
If That Didn't Work
There's a small chance it's the unit's internal fuse. On some models, there's a service fuse accessible by removing a small cover on the plug or the unit's rear panel. You'd need to check for continuity with a multimeter. More likely, the main control board took a hit, which is a major repair.
Heads Up
Always plug these units directly into a wall outlet, not a power strip or extension cord. They draw a lot of current on startup, and a cheap strip can overheat or fail. For future outages, unplug the AC during storms or brownouts to prevent surge damage.