memoQ's activation scheme uses the serial number to tie licenses to a particular physical computer. This means that if you enter the same serial number after installing memoQ on a different computer, the activation server will say No valid licenses when you hit Update licenses online.
But what happens if you buy a new PC? You can enter your existing serial number and update your licenses, provided that a certain amount of time has passed since you last updated your licenses on your original computer.
If you purchased a license, the activation scheme also allows you to install memoQ on more than one computer (so that you can use it in the office and on your laptop as well). When installing memoQ on the second computer, make sure that you change the extra number at the end when you type your serial number. By default, the extra number is "1"; on the second computer, use "2" instead.