Lights are often replaced, simply because the fixture often cost less than a replacement ballast.. and you eliminate all the variables.
Let me explain a bit about how a fluorescent light works. You turn a switch "on," the ballast transforms and saves up the electricity, makes a big spark inside the bulb, and the gas in the tube glows as a result. (Greatly over-simplified!!)
Notice the parts about "saving up electricity" and "making a spark" Lots of things can interfere with those happening.
Even a poor connection can have the effect of making it harder for the fixture to get enough power to make a spark powerful enough to light up the glass.
So can a loose bulb, a bad bulb, bad socket (tombstone), or iffy components in the ballast.
So, in troubleshooting fluorescent lights, the first thing to do is to replace the bulbs with ones that you know are good. It's easiest to swap them between fixtures; if the problem moves, then it's in the bulbs.
Then check your connections. Take off the wire nuts and look to see if there is lots of good copper to copper contact.
Check your supply voltage.
Check the switch- if all the lights arehaving probs (easy to forget if there's only one light on the switch!)
When you changed the bulbs, you got some idea as to the condition of the sockets.
Now- look at the wiring. IS THERE A GOOD GROUND? Electronic ballasts need a good ground to work properly.
Is the ballast wired in correctly? Easy to get wrong- especially with the 'slimline' types.
You've now ruled out everything except the ballast.... so your problem must be there!