AE version 13.6.1 works just fine on my Windows system.
Although, all versions of CC 2015 would launch on my system, so there's likely a bug that was affecting your system that wasn't affecting mine. What would happen when you tried to run it on yours? Also, you can install AE CC 2015 (and update it to 13.6.1) without messing with your earlier versions. See here for how: keeping previous versions installed when installing CC 2015 applications
I have AE CS5, CS6, CC, CC 2014, and CC 2015 all installed on my system at my home studio.