Hi rondini.
Several ways, but I think they won't all help you.
(1)
If you have registered your copy, the license key can be recalled using a special program. But as you haven't installed it on this PC, that won't work for you. Have you uninstalled it from the old PC yet? If not you may be able to extract the license key. Let me know, and perhaps I can help.
(2)
If you registered your profile on this forum, you could simply view your profile and it would be there. But for some reason, you didn't do that previously. So that's no use, either.
(3)
If it was a boxed copy, you could simply look on the packaging.
(4)
If it was a downloaded copy, you would have received an email with the key.
(5)
Failing all of the above, send a copy of the receipt for the game to info@shipsim.com, explaining your problem. Although they are under no obligation to help, I have always found them to be very helpful.