Hellgate Palladium

Hi. I was about to install Hellgate: London on my computer when I hit a snag: the installation required a key number. I have no idea where my manual that held the key is, and I'm now quite frustrated since I was really looking forward to playing the game. I know there is something online called keygens, or something similar to that, and what I'd like to know is if I am able to download a keygen or get a Hellgate key from the internet and use it legally.

Thank you!
It would be simply ridiculous for me to buy an entirely new Hellgate game just to receive a new Key.
I see plenty saying it's illegal. If so, I won't download it. I believe I did register the game so I'll check up on that, maybe I'll be able to get another one. Thank you!