DVI ports come in three main types with the pin configuration different for each
DVI-I - Interlaced analogue and digital
analogue only - very rare doubt you have it
It may be specific to your card as that is quite an old series now but I have not heard of people having an issue trying to transmit analogue and digital signal at the same time. I ran a triple monitor setup for quite a while with 1 vga connection and 2 dvi connections with the same card (8800gts) managing both the vga and dvi signal.
Have you properly configured them in you gfx properties?
Have you tried a third party program to manage the displays? (multi mon (free) or ultra mon (free trial))