Hello Ghostsafe, I’m sorry for the inconvenience that you have faced with your system.
We always recommend using straight connections from the board to the display.
You can also try installing the latest graphics drivers available. From our side the latest drivers are the following Intel® Download Center you may want to check with Dell if they have a newest version.
In addition to that, you could also try another adapter.
I also have a Dell Optiplex 780 and have the same issue. I just downloaded the Intel driver update utility and brought everything up to date. Updated the Dell BIOS to latest revison, and latest Windows updates. Can you confirm wheter or not the Intel Q45/43 express supports audio over the display port? Based on the research i've done from displayport.org they say not all display ports have that feature of supporting both audio and video. I've used different TVs and different Display Port to HDMI adapters. Everything works fine on my laptop when testing and the TV shows as an audio device under the sound settings in control panel...but on the Optiplex 780 the TV doesn't show up at all.
See this link:
As sylvia_intel has mention, we always recommend using straight connections from the board to the display.
This is because these devices need to modify and transfer the signal coming from the system to display it in another connector type and during this process the system can be affected and therefore not displaying the information or sending the signals as it should.