You need dual-link DVI-D. Single link just can't carry enough information for the resolution, it's maxes out around 1920x1080/1200 @ 60hz (depending on suppport), whereas you need much higher than that. (DVI-I doesn't matter for you it just adds the analogue support to DVI-D)
Look at the number of pins on the cable, a single-link cable will look like it's missing pins, a dual link cable will be full.
This may help;http://www.datapro.net/techinfo/dvi_info.html
Dual Link you Want;
Single Link you Don't;