Probably the ballast has gone bad. If you take the cover off, remove the tubes, you should be able to access the screws holding the ballast in. Remove the ballast, being careful to note how it was wired and take to a place that stocks replacements. The other choice is to remove the ballast and replace with 4-5 strips of LEDs.
5M Cool White Light Strip 300 LED Waterproof 5050 SMD 60leds M 12V Black PCB | eBay
This strip of 300 LEDs is enough to replace multiple fluorescent fixtures and reduces power draw to boot. If you search at the top of the page you'll find threads with 'how to' instructions.