2011 Mac Mini not working with included HDMI to DVI adapter
Same problem here with a Specter x20G Naga III monitor. A few days ago I tried to set up a new Mac mini for my wife. There was no video from the HDMI to DVI converter. I plugged the old Mac mini (circa 2007 but updated to Snow Leopard) in and the video worked just fine. I called Apple Care, they made an appointment with me at the Genius Bar, I took the new mini in and, using the same display adapter, it worked fine with their monitor. While installing the software updates at the Genius Bar, that mini kenel panicked. So they issued me a new one.

I brought the new mini home, plugged it in, and I had no video just like the first one. I tried a different DVI cable. No love. I tried another monitor with the HDMI to DVI converter and the video came through just fine. So I went back to the Apple store to pick up a mini display port to DVI converter. It didn't work on the Mac mini. It also did not work on my Macbook air.

My conclusion is that some DVI monitors just don't work with Lion. (Lion being the one commonality between my Macbook Air and my wife's Mac mini.) I ended up buying a new monitor. It works fine with the new Mac mini. I took the old monitor and set it up as a second display on my daughter's Mac mini which is still running Snow Leopard. It works great.