Another obvious question: Are you using the TAB key to advance to ships that still have movement points left?
Yes, I realize these questions are obvious, and most players know about it, but frankly, I am having difficulty imagining what else could be getting in the way.
On the other hand, there should be some way to force "next turn" without having to complete all of the tasks that can block going to the next turn. I tried "CTRL-ENTER", "ALT-ENTER", and "SHIFT-ENTER", none of which did anything I could see. Also, the key substitution map does not list such a function.