Yes you can run both onboard and agp on Most boards, It sounds like the pc got damaged in shipping, Everyone always thinks this is a video card problem Just because there's no video signal,,,it isn't!! it's 99% of the time motherboard related! And what monkey cable are you talking about? If its a 9600xt aiw it should have at least a vga out. Are you sure that isn't just a tv tuner card?
Edit -- my bad it does require a "Monkey cable" lol The guy probably had the onboard disabled when he had this card in it,,, To get it back to onboard just reset the cmos and remove the battery that will reinable it.