You will need 10 players for that setup, but you should be able to use simple DVD players and burn your own video. The trick here will be having players that allow for the video to loop. If not, you may need to create the video of all the videos combined and repeat over and over for a couple of hours worth of video. Then you could just start them at different intervals or make a DVD for each on that starts at different places. Then you could simply restart them all. If you had 10 players of the same type,then a single remote may start them all at once.
Someone else may have some other input on how to get 10 video outputs, but with the need for sound on them .. looks like you will need a unique player for each screen for the desire results.