Problem with Kitchen light

Hi. I have a square light fixture on the ceiling of my kitchen. It has been problematic since we moved in 10 years ago. It has 2 U-shaped fluorescent bulbs. When I turn it on, it usually works. But often, it doesn't, or it takes forever to turn on, or just one bulb will turn on. Both bulbs are good. So I just bought a new ballast, and the problem didn't go away. I'm out of options. Any thoughts as to the problem and how to fix it? Thanks.