The Eyefinity 6 5870 has 6x mini DisplayPort outputs, and has no DVI outputs. Are you sure that's the one you want? I'd think that you should just get a regular 5870 from Sapphire, XFX, Asus, or whatever you can find.
Otherwise, the build looks decent. Based on the newegg link, it appears that the DH-14 comes with fans, as it lists 2 different size fans in the specs.