Using my TV as a PC gaming monitor

I have a 42" Sony Bravia LCD TV, and I've run an HDMI cable from my pc to the TV. This works just fine when I'm using any programs that are windowed. But when I try to get a PC game to output to the tv, it doesn't work. I've tried several different games. I set the TV as monitor 1 in control panel, and set windows to display on monitor 1 (the games only seem to run on the main monitor), but when I launch the game, the TV screen goes completely black for about 30 seconds, then my PC reverts my regular 22" monitor back to monitor 1 and minimizes the game.

I was told that I need to be sure the game's resolution settings match my TV's native resolution, but most games, Skyrim for instance, doesn't go up that high (1920x1080).