I downloaded GSX Demo, and it worked fine on my computer
Of course it did.,
Once I purchased the full software download my FSX crashes every single time it is installed.
THIS IS NOT POSSIBLE. Sorry, but it's not. Have you DOWNLOADED something, to activate the product ? Of course not, the program is bit-by-bit identical and it's NOT modified in any way, it just works in every airport so, it's not possible the Demo version (there's isn't another version, there's only one version of GSX and it's the Demo) would work, and the Full version wouldn't.
But I've already told you this.
When I remove it, the simulator runs fine
That doesn't obviously mean the program is GSX, of course. Since the Demo worked, what's really happened, is that you have installed (or another product, as part of its installation) installed something that has caused a conflict in your Windows system, and this is AFFECTING GSX, it's not the other way around, GSX is the victim of a problem, not the cause.
But in any case, I ALREADY replied to you in another thread, but you haven't done what I've asked so I'll repeat it again:
Before saying GSX is the problem, you should FIRST check WHAT really crashed.
If you go into the Windows Control Panel, under the "Administrative Tools" section, the Windows Event Viewer will have your crash details recorded. Look in the Application log for crashes related to either FSX happened recently, select the crash details, and see what was the error. This could give an hint what really crashed.