Why doesn't DP/DVI cables work with DP in the monitor?

[Whistler]

I have a cable that is DP in one end and Dual Link DVI in the other end.
It works great when used with the DVI end in the monitor and the DP in the computer.

However, does anyone know why reversing the cable doesn't work at all? That is, running the DP end in the monitor and the DVI end into the computer (I did remember to change input source on the monitor).

The idea stemmed from the fact that you can only use two DP ports and must use one DL-DVI when using EyeFinity setups on my 6780. My thought was to use the DP socket on all three monitors, but have one of the cables ending up in the DL-DVI port on the graphics card.

I don't think it is a case of active/passive conversion, as that would be the other way around, meaning to convert a DVI cable from the monitor to DP in the GPU.

[NEC_Art]

There's just a difference in the protocols. DVI can only carry video; DisplayPort is higher bandwidth and carries audio and video.

[Delphium]

DP via the use of adaptors is able to output a number of different signals such as vga, dvi, hdmi and dp.
DVI can only convert to vga ad hdmi without audio.

The cable you are using sounds like a passive cable, not active.
As you say your monitors all support DP, I would advise that you run 2 of the monitors via dp>dp cables and the 3rd monitor via dvi>dvi cable.