Sounds like the cable you have is for taking DisplayPort output and connecting to the DVI input of a monitor. It doesn't work the other way around. What you need to do is get a DVI to DisplayPort converter. For example, this:
http://store.apple.com/us/product/H...single-link-dvi-to-mini-displayport-converter
I'm not sure if that will work with your specific monitor, though, so I would check around to see if anyone has had success.
That is a $130 adapter and only supports single-link DVI (if your monitor is 1920x1200 or less, that is fine, but it won't support high-res like 2560x1440 or 2560x1600). You might be able to find one cheaper than that. But a better solution would be to upgrade your video card to something that has Mini DisplayPort outputs (and then get a Mini DisplayPort to DisplayPort cable, which are fairly inexpensive). Though that would cost more, but might be worth it.
What graphics card do you currently have and which Mac Pro is this?
