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Please see the official X‑Plane Support page for help.
I am not from Laminar Research or XForcePC; just a flight simmer from down under.
My comments are based on the fact you have purchased the official, genuine and original version of X-Plane from Laminar Research and not the 3rd party modified hybrid version of X-Plane.
Have you installed X-Plane either onto the desktop or onto/into a dedicated directory on your "C" drive or onto a dedicated drive just for X-Plane
Have a look at the following link found at https://www.youtube.com/watch?v=V4RjIxrhkXs from Michael Brown. Michael runs a business that builds PCs predominantly for X-Plane. His business is preferred by Laminar Research as the PC supplier suitable for X-Plane in the USA.
Use the advice because he has the experience. Have a good look at the video, especially the latter half, where he discusses the actual installation process.
As a side issue the demo download is the same package as the full package. The demo mode converts to the full mode when you apply the product code otherwise you remain in demo mode.
How much or have you installed any additional aircraft or other software packages onto your system. If none or very few, then it may be prudent to perform a complete deletion of X-Plane and do a fresh install. When you do, use a good reliable software removal package that will perform a "remnant" file check rather than relying on windows uninstaller (or Mac system) software.
If all else fails then attach your log.txt file so others with a greater knowledge base than me may be able to spot a particular cause of your problem.
This site is no longer being actively maintained.