It sounds like the Windows 10 installation removed the profile. What profile are you trying to use? When you go to Print Job> Color Management> Profile> 'Other' does the profile 1) appear in the list and 2) have a check mark next to it?
The entire list is missing.
My options are: managed by printer and other. When I select "other", there is no list, just stays "other".
Thanks for your time.
When you go to Print Job> Color Management> Profile> 'Other' you don't see the below popup window? If so the first thing to try is resetting the LR Preferences file. Follow the instructions at the below link for your specific version of LR (1-5 or 6/CC). BTW what version of LR are your running?