Hi interactivemartin,
As mentioned by Mike, to check the steps mentioned by me, I am putting them here once again for your convenience. Please follow the steps below :
1. Enable root user (Mac) or Hidden Admin Account (Windows) Enabling and using the "root" user in OS X - Apple Support
2. Log in to the Root/Hidden Admin account
3. Uninstall AI with the help of CC Cleaner tool : Use the Adobe Creative Cloud Cleaner Tool to solve installation problems
4. If you are on a Mac, navigate to Applications > Check if you have any folder left behind for Illustrator, if yes, trash it
5. If you are on a Windows PC, navigate to C Drive >Program Files > Check if you have any folder left behind for Illustrator, if yes, delete it.
6. Re install AI with the help of Adobe Creative Cloud app in the Root/Hidden Admin Account itself and then check.
Thanks,
Om