The specific device I am referring to, is the new Surface Dock for Surface Pro 3/4 and Surface Book. I have described the issue here on Reddit, and a number of others are also experiencing the same problem. Basically, the new dock doesn't work when the monitor is connected using mini displayport to HDMI. The monitor is detected correctly and the correct resolution is set, but the screen remains black. In my case, I randomly get some image on the monitor, but it's compressed to one side of the screen and garbled. The mini displayport to HDMI adapter works properly when connected directly to the Surface, so the adapter itself is fine. If I instead connect the mini displayport to VGA adapter to the dock, the monitor displays correctly. I have tried using a straight mini displayport to DVI cable and the issue remains. Additionally, I have connected a Surface Pro 3 to the dock and experience the same issue.
So to summarize, the dock does not function correctly when using a mini displayport to HDMI adapter to connect the monitor, but does work with a mini displayport to VGA adapter. This problem is repeatable using both a Surface Book and Surface Pro 3.