The factory radio affects as many as 3 different fuses. See here for more info: http://www.peachparts.com/shopforum/showthread.php?t=154476

It sounds like you've connected the switched wire to ground or it's loose and shorting something out since the fuse for that wire blows when you turn the ignition on.

I'm a fan of the Crutchfield adapter harness. It plugs into the factory radio jack (no cutting) and transfers the wires to modern industry standard (no guessing, just match the colors).

Search the media section, there's plenty of photos and wiring/fuse issues there.