How to get a TL light working
Flouresent lamps do go bad over time, If you have replaced several starters the next step would be new lamps especially if the ends are dark or black. On older fixtures with mag ballast (requiring starters) the ballast do go bad but I have seen them last over 50 years. If the fixture will not light with new lamps the next item would be the ballast (most of the time it is cheaper to purchase a cheap fixture with a ballast and use the ballast in the old fixture. It amazes me that you can find entire fixtures for 1/2 the cost of a ballast. You may notice quite a bit more light with new lamps I recommend going for 5k or higher color for a true light color where 3k looks a bit orange/yellow in comparison.
When purchasing a new ballast make sure to get one rated for the size and length lamps your fixture uses if saving a high quality fixture. Just thought I should add this if a t8 or t12 4' lamp is in the fixture I have started going with 22 watt led replacements easier than replacing a ballast and more light from what I see. Most of the UL approved. LED retrofits have the neutral on 1 side of the tombstone and the hot on the other side (I get the ones that do not need the ballast) I have completely relamped 2 workshops and 1/2 of my shop at work with these for just a couple $ more than quality lamps cost with no ballast to fail.  Less power used instant on to full power and longer life.  There 18 watt that is supposed to be the same light output as a 4' t8 lamp but the price difference was less than 1 dollar per unit, I have requests to do 6 more areas every one loves them and they don't flicker when it is cold.