Fluorescent lights don't always light first time

[rlk67]

We have a finished attic (finished before we moved in) with a bedroom and slanted ceilings like the shape of the roof. On one ceiling are two separate sets of long-bulb fluorescent lights. The wall switch doesn't always turn them on the first time, it takes many tries, and usually only one set will light. Sometimes both light only dimly. It's like an arcade...are you feeling lucky tonight? The bulbs are good, changing them hasn't fixed the problem. When it comes to electricity, I need a step by step approach of what to try. Thanks.