Sometimes Fluorescents can be repaired.

Compact Fluorescent glass tube

Fluorescent lights are often known to flicker, shut down (light) after a few seconds when they are switched on, give dim light or even no light at all. Sometimes these problems can be fixed, that is if the glass tube is not damaged and its connectors show a very good connectivity/continuity on the multimeter. So our hope to see our fluorescent working properly again is in examining the ballast circuit. The following explanation shows the components that are likely to be faulted when the lamp is not working properly.

Electronic ballast of a Compact Fluorescent Light

When you open the lamp, you will see the ballast circuit inside and you will most probably notice a blown fuse.
Note: fluorescent lights may contain Mercury which is very poisonous. Make sure you discard broken tubes safely. Work in a well ventilated area, use gloves and respirators if possible. You may also read about how to clean up a broken fluorescent.
In the ballast circuit: 

• the fuse often get blown when the rectifiers or switching transistors get shorted. So they all have to be checked on the digital multimeter to make sure they are working properly.  If not working, first replace them (the rectifiers and transistors) and then replace the blown fuse.

• Sometimes the fuse can blow due to a shorted inductor, replace the inductor if possible. 
• Dim light, light goes off after a few seconds or no light at all, this is caused by shorted capacitors (ceramic and electrolytic caps). So all these must be checked in order to repair the lamp.