I have a Sharp model LC-42sb45u that will not turn on since power outage.

Voltages sometime increase/decrease during power outages. This mainly afftects the power supply of a lot of electronics equipment.
1. Check the fuse.
2. Check primary components like; Bridge rectifier, filter cap, switching components etc.
3. Check secondary (cold) side once you isolate the primary side to be ok.
Please consult a professional technician if you are not skilled in electronics repairing.

All the best
Rjn