External GPUs still get bottlenecked by most external interfaces, meaning they aren't that great for gaming. The only external interface that is really fast enough to not horribly bottleneck a gaming GPU is Thunderbolt, and Thunderbolt ports are something of a rarity on PCs right now. Thunderbolt is an Intel proprietary technology, so you won't have it on an AMD system. It is also currently only available on Apple systems, higher end Intel motherboards, and certain Intel based laptops, mostly Ultrabooks I believe.
There recently was a Thunderbolt based enclosure for GPUs released, the problem is it is very expensive, like $600 expensive. All told, just install a GPU internally with the PCI-Express slots. If your PCI-E slots aren't working, replace the motherboard, that is the most cost effective solution for you.