Upgrade from Vista Home Basic to Vista Home Premium

My new Dell Vostro laptop had Vista home basic installed and activated. I
purchased the upgrade for Vista Home Premium. I received the upgrade DVD
after about a month of non-receipt of the DVD after the order was placed.
The link provided for the upgrade which I guess was for the product license
key expired and I couldn't use my verizon.net email address to create an
account to access the digital locker so I proceeded to install the upgrade
from the DVD while waiting to get instructions on how to access the digital
locker.

The upgrade appears to have completed normally after about 90 minutes of
installation time with no error messages but I only now downloaded the
license file from the digital locker.

Vista asked me to activate the software, which I did with no error messages.

I was subsequently told that my operating system would probably stop working
in a month. If I change the software product key to the product key number
provided in the license file, should the software work normally?

Or will I need to do something else?