Someone on IGN, for some reason, got the idea to try this and it worked for him. I tried it as well after reading his post and it worked for me, which made me assume it worked for everyone. Apparently some Doom 3 CD keys are duplicates of Prey CD keys. I feel bad now, even if it is a sub-par game, but I don't think there is a way to unregister it.
You gotta admit though, the first and last hours of the game are brilliant. The boring bit in the middle which consists of most of the game is rather repetitive though.