I had a feeling Trent would do something like this.
If your song is chosen, you'll win airfaire to LA for two, two nights in a hotel and tickets to the screening of "The Social Network" on premiere night (this suggests that you wont be going to the actual premiere, just seeing the movie on the same night.). You'll also probably meet Trent and Atticus Ross as well.
However the catch is that the deadline to submit remixes is next week, Sept 28th. Which means if you are interested, you have very little time to show off your remixing talents.
So get going. To download the tracks, go to http://remix.nin.com/