What I have is a DVI-I (Integrated) Dual Link Female on my desktop, and a cable from the monitor with the DVI-D (Digital) single Link Male connector.
Ok, a DVI-D single link cable is made to be able to plug into a DVI-I port. If it's having a hard time plugging in you may want to check for bent pins on your cable. Try to see what isn't lining up and is causing the problem.
There's no such thing as a DVI-D to DVI-I adapter because DVI-I can support every type of DVI cable, I, D, and A. Other than that you may just need to buy a new DVI-D cable for the monitor. I can't think of any other reason why they wouldn't connect.