So let me get this straight you have display 2 and 3 connected via a DP to HDMI cable, but when you connect screen 1 with a similar cable you get no video? That is because the 6990 only has 2 video clocks, and required the use of an active adapter for a third display. If using the active adapter dosen't work, then report back.
DVI to HDMI on screen 1
DP to HDMI on screen 2 (passive display port adapter - comes with card)
DP to HDMI on screen 3 (active display port adapter - non powered, you don't need the powered one unless you push above 1980x1200 res monitor)
When I change screen 1 to DP to HDMI (like the others) I get no video. Basically leading me to believe I need to have DVI always connected.