Offline installer

Check out what is listed in "View my subscriptions". 

Since you have installed F-Secure to your new machine, connect to the Internet  with the license number you want to move.

You will be automatically be connected to the F-Secure license server which will hopefully tell you the license is associated with another computer and asks if should it be changed.

If this does not work;

Try the Official F-Secure support here; http://www.f-secure.com/en/web/home_global/support/contact/request

or you could also have an online chat with a F-Secure expert; http://www.f-secure.com/en/web/home_global/support/contact/chat

Either should be able to reset your license.

Let us know how you get on.