First, this sort of problem is often a broken lampholder ("tombstone"), or failing to get the bulb to seat correctly. The tubes have little "tick" marks molded into the metal end caps to help you see when the pins are square-on engaged.
However it is also possible for a ballast to be broken. Ballasts are pretty easy to replace, if you pick the correct replacement ballast so the wires just match up. For that, you'll need to take the bulbs out and look for an access cover to get to the ballast, remove that, and shoot us a pic of ballast and the 5-8 wires coming out of it. Sharp picture of the label wiring diagram will help too. (yes, I'm aware there won't be any light in the room lol).
A new ballast will be silent, start in the cold and never, ever flicker. That, with the new ~90 CRI bulbs you just bought, you won't believe it's the same light!
Once you're "in for a penny, in for a pound" with a ballast replacement, there are 2 possible upgrades to consider.
- T8 real fluorescent, which uses T8 (1" diameter) tubes and a T8 ballast. They are about 25% more efficient, but use a different ballast that is incompatible with classic T12 (1-1/2" diameter) tubes. These tubes last a VERY long time.
- LED replacement "tubes", which are even more efficient, but the wiring is weird and hard to explain. The light isn't quite as good as real fluorescent and the reliability is much worse than it ought to be. Just look at the ceiling of a big box store that has converted (and they're buying the good stuff, not the Chinese crud we consumers have access to).
If you're interested in either upgrade, just ask.