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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.