Thanks for getting back to me.
After spending hours on google, I found some advice saying that de-activating and re-activating some of the services (AXL, etc..) may help. Just as I was about to do it, I had a peep over at the phone and EM was requesting the user ID and PIN. So it worked.
I named my profile 7961_EM and the other profiles were similarily named with the only special character being the underscore '_'. Do you think that this may have been a problem?
I also read that if I moved the CUCM server to another network (giving it a new IP) can cause issues as there might be some residual reference to the old IP. Cisco documentation says to remedy this, click the 'update subscriptions' button on the service configuration page, CCMadmin -> System -> Service Parameters. When I did click it, a window popped up saying that 'updating subscriptions may take hours'.
What do you reckon?