I am not from Laminar Research; just a flight simmer from down under.
Have you made an official purchase of X-Plane from Laminar Research? If you have then you would/should have been supplied with the product key. You haven't indicated that you have officially purchased X-Plane.
I am of the opinion you currently have two versions of X-Plane on your PC despite the fact the demo version is the same as the full version. The demo version can become the full version when you apply the product key.
My suggestion is to delete all files associated with x-plane no-matter where you have installed the software on your PC.
Then download the full version again and apply the product key when prompted to do so during the installation process.
Alternatively download and install the software and when you start X-Plane you will be asked if you have a digital version. In your situation It will prompt for the product key. If you miss this process you will be asked if you have a disc version and ask you to install disc 1. As you don't have a disc version you will be advised the software will revert to a demo version.
The demo version has a fixed location and will give you a 10 minute time limit. This is the reason you received the ".... time expired" message.
As a sideline issue with the digital version you will need to be connected to the internet at all times as the software performs some silent background verifications that you have a legal copy and you are not running more than one copy of x-plane at the same time.
Hope this helps.