Will a Radeon 8500 64Mb 4X AGPrun on a new Asus A7N8X-X 8X AGP 3.0 slot?

Yes. It will run on the Asus A7N8X-X. The Radeon 8500 64Mb 4X AGP supports AGP 3.0 standard. But there could be some compatibility issues, when this card is used with some optical drives and certain memory cards on the same board.