I have the same problem when I first load up a turn report, all systems appear to be locked. Once I click on one of my ships in a system, then back to galactic, everything is fine. Galactic turns are supposed to process about every 6 (?) hours. System turns process at 48 hours, or once every race in-system has submitted orders. So if you are the only race in the system, you can take a turn in that system every few minutes or so.