Q: rented movie freezes after 10 minutes, green screen comes up

Howdy nyc1787,

Welcome to Apple Support Communities.

If I understand correctly, there's an issue playing back a movie that you rented with iTunes on your PC. While this article below doesn't address the exact issue that you described, it does provide a lot of great troubleshooting tips that should help you resolve the iTunes video playback issue on your PC.

Fix unexpected quits or launch issues in iTunes for Windows - Apple Support

Also given this is a rental and you've already started to play it, that means there is a 24 hour time period for you to finish it.  I suggest you report a problem with the rental by using the link below, and then follow the aforementioned troubleshooting.

Report a problem with an item purchased from the iTunes Store, App Store, Mac App Store, or iBooks Store

Ciao.