Had a new experience that I think is regarding this issue today. I decided to hook up my TV to my Mac Pro (my main monitor is connected through DVI port).
I connected my Computer to the TV via the mini-display-port with an Apple connector. The other cable was a DVI to HDMI with the HDMI end going into my TV.
I have done this several times with different macbooks, macbook pro's and iMac's with the exact same setup and had no problems whatsoever.
The result was a blank screen, no signal. So I thought OK I'll try the other port, same result.
I then tried both the mini-disp. ports withouth my main monitor connected through the DVI port, still nothing.
I then tried my main monitor with the DVI to Mini disp. port adapter in both ports and nada again. Switched my main monitor back to the DVI port and got a signal.
The only thing I did not try was the HDMI to DVI cable from my TV to my comp straight into the DVI port since I had already tested the mini-display-ports on my main screen and neither worked, since my main screen works perfectly through the DVI port (and other computers work on the TV) I can safely assume that neither mini-ports work.
Could this be related to the snowy screen and other issues with the 5870?
*edit*
I tried the following with a good result:
Connected the TV via the DVI port, worked. Then my main display via the mini-display-port at the same time, nothing on the main display.
Then I turned the main monitor off, switched it to the other mini-display-port, turned it on and whilst doing that clicked "detect displays" and then boom the TV changed from "screen 1" view to "screen 2" view (dock and desktop icons was gone, wallpaper changed to default). And when the main display came back on it had my "Screen 1" view.
Strange stuff, had my TV connected to mini-port and main screen on DVI and clicked detect displays 10 times with no effect.
Also note I am only using two displays so this is not related to the three-display problem where you need the 99$ dual link connector.
*edit 2*
I have now moved screen-connectors back and forth a few times to try to figure out what the problem was, I finally managed to get my TV on the mini-port and main monitor on the DVI port at the same time. 2nd mini-port is still not "active" but I guess I could force it to be by moving stuff back and forth more.
What I learned was this: The ports do not work like they do on a laptop where you just plug it in and it pops up. Seems like you have to "activate" a port, and when you do it remembers that you prefer to have your desktop at that specific port (or it remembers it by the screen name/id/model/whatever).
So now that I have "activated the mini-port closest to the DVI port I can plug my TV into that port and it pops up, no detecting or fancy-schmancy stuff needed. If I take it out of that port and move it to the other mini-port furthest away, nada.
Then again this can all be a random bug the first few times I tried to connect my TV. If noone else experiences problems with two displays I'll just assume it was a freak thing
