^But did your game really need to be Star Trek? Was there any reason you couldn't have changed the Trek elements to something else? I've seen a "generic" version of the early Star Trek computer game, that one where you moved around a rectangular galaxy made of dots and typed in coordinates to shoot at Klingons, where the names were changed but the gameplay was the same.
Like I've been saying, fanfic isn't the only option. If you can't legally use someone else's ideas, you can just use your own.
Filing the serial numbers off can be quite lucrative. Just google E. L. James.