I am so glad that the Zorin community, is building with many wonderful people. I was done with Windows nonsense, when Windows 10 came out, and they deprecated Windows7, making it impossible to fix my old computer, forcing me to switch to Linux.
Regarding the issue you face, check your computer's bio's, to see if it lists any power management features. Its odd to hear on 2 operating systems, that power management didn't eventually put the notebook to sleep, and thats what made me think of the bio's in the first place.
Additionally, you can gain more power management features in the OS, if you use XScreenSaver. Here are the steps to set it up...
Then after you do all that, go to the advanced tab, and you will find the settings that you can enable and adjust, your display power management.
