Would it be possible to get a PCI to PCIe (I see them available for sale online) cable and be able to connect a GPU to it? I know it's possible to DO, but is it feasible performance-wise for bitcoin mining?
PCI and PCI-E are completely different busses. Different signaling, different protocol, different everything. You can't get a "cable" to go from one to the other. Startech does, however, make a low profile card that goes into the slot first, and another card plugs into it. It's a weird bastard adapter, but it works.