1. Uninstall the 777 Captain.
2. Reboot your computer.
3. Reinstall the 777 Captain (use the 'Run as administrator' option for Vista/Win7/Win8/Win8.1)
4. Reboot your computer.

Now....You might need to run FSX as an administrator. Especially if FSX is installed in C:\Program Files! I run FSX using the 'Run as administrator' option all the time, even though my FSX is installed well away from C:\ and C:\Program Files! My FSX is installed on another drive and partition (J:\Flight Simulator X)).

For instruction #1 - You might need to do a complete uninstall. See KB #685 for full details (Check-in to Your Profile > Product > Customer Support > Search KB). If you do that:
For instruction #3 - Try using the Manual Offline Activation option. 1) This will allow many activations, without exceeding your activations (it only counts as one activation). 2) The chances are that it will succeed, whereas the Instant Online Activation may fail.

Hope this helps