Well, this doesn't make a whole lot of sense. But to hopefully answer your questions:
1) You cannot "upgrade" the slots on any motherboard. The slots it came with are attached permanently, and they're what you get, forever.
2) Is this your computer? http://www.newegg.com/Product/Product.aspx?Item=N82E16883108198
If so, it does have a PCI Express x16 slot.
3) Just about any graphics card for sale today operates on the PCI Express x16 standard. That includes the HD4670. However, they do also make the HD4670 card for old AGP slots, so make sure you're buying the right one.