I installed Witcher 3 (PC version) from a new CD set that I bought on Amazon. The installation was completed. When I try to launch the game the GOG site appears but my game is not showing in the Library. How do I start this game?

I must also say that I bought the game when it first released and I played it with no problems. I had a system crash a few months ago and had to rebuild my system. So this is a second time installation - in case that matters.

I don't know why the game worked back the but not anymore but what version of the game do you have installed? If you installed the game with one of the first CD versions you probably need to install a patch to run the game since the old CDs miss a patch that you need to run the game.
If you haven't already done so you should activate the CD key you got with the game here at GOG and download a new patch.