When my computer is idle for a period of time Plex shuts off.

My operating system is Windows 7 Home Premium

After doing what you asked I get the following:

Then I get the following, The older version of plex media server cannot be removed. Contact your technical support group

use the Microsoft Fix-It! linked on this page to help with the uninstall:
https://support.plex.tv/hc/en-us/articles/202967086-Windows-Errors-trying-to-upgrade-install-or-uninstall-Plex-Media-Server