I just built 3 rigs that are almost exactly the same as yours, just different brand motherboard (ASRock mobo, Sempron 140, 2x Radeon 6950). I'm also using Ubuntu for my rigs. I had no problems simply putting both cards in and starting the install with a monitor plugged only into the top card (the one in the real 16x slot). I'm not using any dummy plug in the second card. Also not using CrossfireX connector.
It sounds to me like the most likely issue is some default setting on that motherboard that is messing with the default video card when two are connected. Have you tried plugging your monitor into the second card (and on that note, have you tried some of the other video outputs on the two cards)? Also, dig through the bios settings to see anything related to the default video device. Sometimes it has settings like PCI-E, PCI, Integrated, etc. Try some different settings from the default.
Also, if you're using crossfire, try without. If you aren't, try with the crossover connector. Basically trial and error every option you can think of.
One other thing I just thought of, what happens when you start the machine with only one video card in, but in the second PCI-E slot? Could possibly be a bad slot?