I was working in the basement during a thunderstorm, with two banks of fluorescent tube lights (like office lights) in two rooms on. Thunder pealed, power went out. Every so often there would be a flicker of light, then it was gone again. Went upstairs, discovered power was on upstairs (although newly installed fluorescent bulbs are much dimmer in one room). Returned to basement, checked the circuit board, which was fine. Discovered the incandescent lights and the wall outlets all worked. Hour later, and still can't get the fluorescent tubing to turn on. What happened?
They all went out at once? It may be a loss of power to the lighting circuit, or it may be a power surge taking out all the fixtures. If the power to the fluorescents is good, then it's one of two things:
the fluorescent tubes ($2-5)
the ballasts ($15-25) -- a ballast is an electrical module inside the fluorescent fixture which controls the power for the tubes. Fluorescent tubes take specially regulated power, not common mains power.
It's more likely the ballasts than the tubes, but the tubes are easier to swap. There are Q&A on here which discuss at length identifying and changing ballasts.
Fluorescent tubes are now very good, and no longer give the green flickery sickly looking light they once did. If it is the ballast, however, you may want to price out switching to LED replacement fluorescent "tubes". Make sure to get direct-wire types, not the kind dependent on ballasts.