The Flightbeam installer is not exactly the same as our very latest versions, so it's using the Co-existance key, and then it might be confused by having removed FSX after installing FSX:SE, which is FIXED in our installers.
In your case, it seems that something is changing the Co-existance key and set it to 1 (you said yourself the problem "fixed itself", so it's clear your Co-existance key was correct at some point, but then it changed), so our installer is mislead thinking FSX is there *together* with FSX:SE, so it must use the FSX_SE folder under %APPDATA%\Microsoft, which is not the correct one if there's no FSX.
You can activate logging in the installer, to see what’s wrong in your system.
- Open a command prompt ( start -> CMD -> enter )
- go to the folder where you have the installer, for example:
CD c:\Users\Yourname\Desktop
Assuming you put the installer on the Desktop
- launch the installer with this command:
gsx_fsx_setup.exe /log=install.log
This should hopefully create a file named install.log on your Desktop, after you close it. If you have it, then send it to me.