You could use extended or cloned mode for 2 displays.
Cloned mode means the same picture on all displays using the same resolution and same refresh rate (24hz,50hz,60,75) and that could be a problem if any screen don't use any resolution (1080p) or any hz (24hz) that going to be used.
Extended means that you do not have to use the same resolution and refresh rate and that the desktop is extended to the right or left or up,down from the first display.
The problem with extended mode on windows is that windows REALLY want too use the screen using the hdmi port as nr 1.
In my experience using ati,nvidia,intel graphics is that windows is sorting the diffrent ports in this way.
3vga or a dvi port with a vga adapter on
Displayport i don't now about (only use 1 screen on my gaming rig that use Dp port).
I have not used componet at all so don't now how win handles that.
I had a pc that was used for surfing,torrents and as a htpc (i was using a dvi to vga adapter to monitor (crt) and a dvi to hdmi adapter to tv (it was a dual dvi out)) a while ago.
And whenever i inserted the hdmi cable windows switched the nr 1 screen to my tv it no matter which dvi port was used for hdmi 1 or 2 it still changed over every damn time.
So every damn time i have too go and change the nr 1 screen back to the monitor.
That can be done using ati ccc or nvidias control panel OR use windows own.
Right click the desktop (screen nr1 with the windows taskbar probably the tv (you could rightclick on the other screen but it will only show up on the nr 1 screen anyway))
and choose screen resolution and there you will see what screen is nr 1 right click on the monitor (not the tv) and change the monitor to nr1 after that you must answer yes to keep the new order (NOTE that the yes or no question window will be shown on the now nr 1 screen namely the monitor).
That was a real hassle for me as i had the tv and monitor back to back with a wall between (diffrent rooms) so i had to use a wireless mouse on the tv and then dash to the other room going through 1 room on the way and throw myself at the return or space key and usually (about 2/3 off the times) make it with 2-3 sec left
And yes i only had 1 hdmi port on the tv and no reciver at the time so had to switch cable all the time.
I'm pretty sure that is your problem.