That is a strange one.  I'd recommend that you try to verify it through Impulse first.  To verify the application through Impulse:

-Launch Impulse.  Right click on the entry for the application and choose "Verify Installation"
-Impulse will check the integrity of the installed application.  You should be given feedback as to the state of the installed application.
-If errors are found, an update should be made available in Impulse.  This is not an update to a newer version, but simply Impulse using the update mechanism to replace corrupted files.
-Once the update completes, reboot your PC.

Something else to try if that doesn't help would be to delete your Game.Prefs file from the Documents\My Games\Gas Powered Games\Demigod directory and try loading the game again(note: this wipes out your game settings and off-line game favor as well).

If the issue continues, you may just want to try reinstalling Demigod.

My friend has had this happen 2-3 times to him but I haven't ever seen it.  I believe he's finally figured out that pressing one of the buttons on the numpad (don't remember which one) will cancle the spin.  I'll ask him exactly what he has to do.