Adobe InDesign CC needed Admin privileges to install which is fine but it seems to need the same just to start-up and run the program.
I've given the user Local Admin but that didn't fix it. I don't want to have to 'Run as Administrator' every time they want to use the software, does anyone have any ideas for sorting this?
Without proper system info and other details nobody can even begin to guess. Chances are that your network configuration is to blame and due to using specific ports that are also used by the activation system they are somehow tied together. Well, whatever. This is most definitely nothing that can be solved from within the Adobe programs themselves. Run a network monitor, find out what's wrong and fix it accordingly.