Sounds to me like it might not be a bad alternator, but the pulley may be too large. Try hooking up a multimeter to it and rev the engine, if the voltage goes up when you rev it, you just need a smaller pulley. And I don't think it does much use when you take it to advance auto and have them test it, their machine only measures amperage, not voltage. Think of amperage like your amount of gasoline, and your voltage like your fuel pump. All the gasoline in the world is useless if your fuel pump can't pump it at the sufficient rate. Thus, you could have a 200 amp alternator and it might not be putting out the correct voltage. I've been having some alternator problems with my truck and have learned a hell of a lot about them. I ordered a 200 amp alternator, put it in and it was only charging at like 11.5 volts at idle with all accessories on, when I reved it, it shot up to 14.5 so the company sent me a new pulley (smaller) which I have yet to put on so we'll see how it goes. And while you're replacing your cables, I'd go with at least a 4 gauge wire from your alternator to your battery.
P.S. I would not rely on a lot of the things the computer says, it's said a lot of things to me like "low washer fluid" when it was full, and "low engine coolant" when it was full also.... and in my truck, there's a volt meter on the dash, and it says only about 12 volts when I check it with a multimeter and it says 14 or 13.9 or so.
