In the event that with a new bulb and new starter, the fluorescent bulb still won’t light up, your best bet is to check the ballast. With a screwdriver, take out the ballast and survey for any oil leaks. Install new ballast if the current one is leaking oil. If it isn’t try to check the system for any loose connections.
Testing a ballast for a fluorescent light fixture is a complex task. If a fluorescent bulb is not lighting, and does not light in a known good fixture, then the ballast may need to be replaced. Some great technical information about fluorescent lighting can be found at http://members.misty.com/don/f-lamp.html,