Sailboat ,, cockpit storage lockers ,, I want to paint them so they will be
cleaner, more presentable and protect the finish.

Problem ,, as far as I can determine, they haven't been painted or
anything in YEARS. They are DIRTY. I tried to
clean them but didn't have much luck. I can wipe them down.

Is there a paint, such as Bilge Coat, that will stick to a not very clean
surface?

What paint? Etc?