Sorry but, no one talks about broken parts, want need to know what kind of cable.
Kronos actually has a valid point to talk about broken parts. It may well be that the digital drivers (not software, but signal drivers) of your mini got fried. DVI-I's analog part is just VGA redirected to the DVI conector, DVI-D is the digital signal, but of course that signal needs some driver ICs. Those may be broken. Not nice, but may happen.
On my Mac mini it is all okay and normally DVI-D works just by plug and and play. I use a Dell 2209WA connected digitally to may Mac mini G4, cable is the included DVI-I duallink cable of that monitor. Sometmes ync gets lost for a moment, I think that's a common weakness with Mac minis and high resolutions.
