The proof of your license is your product key. If you bought a commercial computer (as contrast to one you built yourself), there should be a sticker somewhere on the computer's case that shows the product key. Many commercial computers actually have the installation disc as an image on a partition of the hard drive. Have you checked out the possibility that your "installation disc" is actually on your hard drive?
Somewhere along the installation process, the program will ask for your product key. If you do not supply a valid product key, the installation will stop.
After the installation is done, you will be asked to activate XP. If you do not activate the OS, you likely will not get to install the updates. If your product key is invalid (as determined by Microsoft), certain features of the OS will be modified to annoy you and you will be requested to supply a valid product key or contact Microsoft.
As long as you use your own product key, you likely will be able to reinstall XP successfully. (You may need to find drivers specific to your machine.)
If you use a modified version that does not ask you to supply the product key or activate XP, Microsoft may eventually figure this out during one of the auto-update sessions and deactivate certain features in your OS.