I cannot speak for the Steam version, but the retail version works just fine with game. The updates to the game are identical so I would venture a guess that the trainer is not the issue. Follow the trainer troubleshooting guide and see if the suggested steps help.
Well if you look in the troubleshooting guide it says that steam sell slightly modified versions of the game in order to be downloaded and played without the disc. And it also mentions a no-cd 'fix' so how can I find that?