2001 Kia Spectra Alternator or what?

Electrical problem
2001 Kia Spectra Automatic

Ok, to make a long story short, we have changed the battery 3 times. The last time we had the car checked by computer at AutoZone, it said the alternator was bad so we replaced the alternator. I did read that this is the typical process when the alternator on Kia's is in the process of going bad. We have replaced the negative battery cable and the terminals for both posts. All cables seem to be intact and with no corrosion or worn spots. The problem is the car still won't hold a charge. When attached to another vehicle via jumper cables, the car starts immediately and runs like a charm. Within a minute of disconnect, the car stalls. It seems to me that the likely scenario is that we have gotten a bad alternator. Does this sound right or could there be other parts that we need to check or replace that could be interfering with the charging process. We really don't want to have it towed if it is something easily replaced and obviously it won't run long enough to drive it anywhere, so we can't have the alternator tested again. Your thoughts?