DVI-A to DVI-I Result: - Use DVI-A to DVI-A
Both your source device AND your display device are capable of handling analog signals so for this situation you would use a DVI-A Cable to connect the two devices.
If you wanted to use the superior Digital DVI transmission you would need to replace your DVI-A device with one that supports either DVI-I or DVI-D.
These are the cables you may need and some adapters you may find useful for your application.
DVI-A Analog Cable
DVI-A Extension Cable