A couple of things to try.
First, do a full restart of the computer, not a reboot. Let it power off for 15-30 seconds before restarting. There may be a conflict in the memory somewhere.
Second, try opening Windows Explorer and navigate to this location - C:\Program Files\Microsoft Games\Zoo Tycoon 2. In this folder, you should see a file labeled zt.exe - double click this and the game should open.
If neither option works, you may need to uninstall and reinstall the game.