what determines how long the clock shows up when you press turn

Probably it's waiting for you to do something. This can happen if you have events to view in the planet data screen, if a colony ship on autopilot has reached its destination and is waiting for you to choose a star, etc. 

Soooo. . . . .

How do I find out what it is wating for?

The event queue seems to provide little Help.

I often have this happen for no apparent reason. Not sure if it's the same for you, but everything seems 'stuck'. (I can tab through ships but can't actually move any of them) All I have to do is double-click on any planet and it goes away, and I can proceed with my turn.

yup -- mine locks up often if i reload the same game several times to experiment with various actions. I close and re-launch.

Probably the first thing you should try is to click on the "Find" button and see if it shows you a ship to move.

It has happened to me too, but always have been when an event is about to happen, like when you get the 100 corvettes. BUt I just wait and it eventually comes back to life, and Mr. Derekflint by using stupid words don't expect for people be kind enough and answer your question the use of "wtf" is way unnecesary, everyone is willing to help, but don't missuse or abuse the kindness of the people that come here. You are not the only player here and by using that kind of language will go against your own benefit.

I've been experiencing exactly the same problem, with the computer seeming to wait indefinitely, but none of the suggestions above make any difference. The only thing that sometimes works is leaving a diplomacy screen open, but this doesn't always. Does anyone know of a more general solution?
Thanks.