Resolved.
Issue seems to be caused by Zonealarm for me also.
But simply turning ZA off isn't enough.
I have managed to get it to work by un-installing the ZA Toolbar, then setting the "ZoneAlarm LTD Toolbar IswSvc" service to manual. Then after a reboot and exiting ZA from the right-click popup Arma 3 will finally start.

ZA can then be restarted or the computer rebooted to restart it - this saves having to remove ZA altogether.