Upon starting Bioshock Infinite when it goes to full screen my monitor stays black and displays the 'No Signal' warning in the blue box then goes onto stand by. The music and sound plays during all this.
As soon as I minimise everything goes back to being fine on the desktop.
I had the same problem with 'The Wolf Among Us' recently. I hit alt+enter to go to windowed mode and adjust the display settings which worked, however I cannot get it to window mode for Bioshock Infinite.
No problems in any other game I tried (Bioshock 2, TF2, Dear Esther, Amnesia).