Keeping the jumper cables on for a while to sorta charge the battery was good. I don't believe you killed anything by doing what you did.

It's possible you got a bad alternator, that's been known to happen... Even AutoZoned has a warranty, right?

Make sure all your connections are good. You need good solid connections at both ends of all the big cables. Including the ground cables. Including where the wire itself is attached to the clamps. Check them all...
- battery (+) to starter
- battery (+) to fusebox or ??
- battery (-) to ground
- engine/tranny ground cable to chassis
- alternator grounded solid thru it's mounting bracket

Got a voltmeter? Charge up the battery again, run the engine. Measure the voltage across each of those wires. They should be really small, much less than a volt.