The Mac Pro (Early 2008) should be able to work fine with the Samsung 226BW monitor, using any standard DVI cable. Any of the optional graphics cards on the Mac Pro will happily drive the 226BW at it's native resolution of 1680x1050 without any trouble (that's the setup I was using on my nVIDIA 8800GT equippped Mac Pro until I recently upgraded to the Samsung 2493HM monitor).
If all you are getting is a blank screen then check the input selection menu on the monitor (set Auto Source to Manual then use the Source button to cycle through the inputs, remembering to pause on each one for a few seconds to see if the picture appears).
It is possible the cable is faulty - you should check both ends of the cable carefully to ensure there are no bent pins. If there are, you can generally bend them back straight with a pair of pliers, but be gentle!
If that doesn't work, try borrowing a DVI cable off a friend to see if that works. Alternatively, use the DVI to D-Sub (VGA) adapter that comes with the Mac Pro to allow you to plug the cable into the VGA port on the monitor to see if that works. I'm guessing you have tested the monitor with another PC or laptop and it's working ok?
