I have a problem when I play demos. I launch the demo with a demo player, it opens the game and launches the demo, but the demo doesn't work right away. The players run but they don't move anywhere. Runs but actually doesn't run. Stationary running. But then the demo works in about 2-3 minutes...

 

But ain't nobody got time fo dat.

It seems that the demo player you use - MW2 Player or some other weird name they use - has an option to automatically to the command required to make the players move immediately. Hit the Enter key while in-game.

Also, this is a known 'bug', if you actually use a proper command - like '/demo demoname;wait 5;demoback 1' - the demo will automatically play with the players moving.

 

If this demo player doesn't work with that 'Enter' key function, I would advise you to use the command above, replacing 'demoname' with the name of your demo.