When I reinstall GSX there is no window with ask for serial number, and GSX starts in trial version.
First, you should never put your order details on the forum (that's why I've edited your message), and these questions are really more suited for email support.
In any case, nowhere is indicated that you are supposed to see a serial number when you install: since the installer can work as trial, it wouldn't be very useful to have an installer that ask for a serial number.
As clearly indicated in the installation guide ( fsdt_install_guide.pdf under the fsdreamteam folder ), to reinstall and a previously purchased product, you have to use the "Register Serial" function of the Addon Manager menu, which will ask for your Serial Number to be activated.