Disabled turn button

Look for a ship that has "auto attack" turned on. In order to preserve the option of preserving your ships, auto attack pauses whenever the auto attacking ship takes damage, ostensibly to give you a chance to turn auto-attack off before your medium sized ship picks a fight with 2 hp left. If this happens during the automatic movement that takes place after you press "turn," it looks like the game froze.

Simply selecting the ship that paused will cause it to continue to auto-attack (which defeats the original purpose of the behavior) if you can't find it, find any ship that has movement left and give it an autopilot order. The ship will move right away and when it's finished the rest of your ships will start moving again.

Alternatively, click "find" to highlight ships that have not yet moved, and hit the spacebar at each one that comes up. This manually expends any movement points the ships have, allowing the game to move on to the next ship.