Yeah I know how to fix that one.... I have had ATI cards as long as I can remember, but they have this nasty habit of defaulting to a desktop out but no video output.
Go into Display Properties > Click Settings > Advanced > Displays > It is going to show your monitor and your second display / tv, the second display... each one has 2 sub options, they both have icons, 1 has a circle, other has 2 squares on top of each other. What you want is to check in the Circle for BOTH displays, as without the circle checked in there will be no video out....
Trimidium
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