you've changed the bulb and starter, I would change the ballast.
Dave is correct. The ballast is the only thing you have not replaced, although a bad ballast usually blows out an new bulb with a bright flash.
When all else fails, get the short undercounter floresent light fixture from home your improvement store.
Has bulb, ballast and starter all in one, for about $25.00. Does not come with light reflector sheild like you have now, so you may have to add tin foil inside the case or paint it white.