Did you try starting it "manually", so to speak? IE: Clicking on the FSX.EXE file?
If you did, have you tried starting it from your Steam app? Sometimes it needs to be for some reason.
Also, are you logged in to Steam, or just have the app running? Try it when logged in.
You don't have to be, by the way. You can start it in "Off-line" mode with the menu in the upper left corner of the app.
I don't know if any of those are any help. I start mine with a short-cut on the desk-top, and I always start it as Administrator. You can set the shortcut to do that automatically. If you want to know how, just let me know.
Just shooting in the dark here. Hope I hit something...
Pat☺