FSX runs best with NO COMPATIBILITY checkmarks at all, which is the default install, and the Addon Manager doesn't run if you enable any of the compatibility checkmarks too. Everywhere on the forum, we always tell to turn OFF ANY compatibility mode.
If you had to enable a compatibility mode to run the Addon Manager (which normally only runs with no compatibility checkmarks enabled), this is probably just an indication you have some kind of problem with your Windows install, most likely missing/corrupted system libraries, most likely the Visual C++ runtimes, that might have been missing/corrupted due to another product (even non-FSX related) you might have installed.
As explained in many other forum threads, try to remove ALL the instances of the Visual C++ 2005 runtimes using the Control panel, then reisntall any FSDT product which will automatically reinstall them.