If you've eliminated the possibility of an amp and already grounded the radio behind the dash, I'm stumped!
If you do go about replacing the speaker wiring, try the door speakers first. I've never had it cause an issue, but I've seen wires in the rubber boot thing that goes from the dash to the door have the insulation worn off on one side of the bundle from the friction of the door opening/closing constantly. The rear speaker wires are usually in the door sill's and don't have a lot of stress put on them.
Hope that helps!