Q: Car stalled while driving.

My girlfriend was driving to work, and she said all her warning lights came on and her car died. She pulled over on shoulder, when I got there I tried to start it, would not turn over, could here some clicking. We called tollway assistance, he came out and hooked up his car starting unit, he let it charge for about 8 minutes. Car started right up. She drove it to her job site while I followed. I took battery out and took it to AutoZone to have it tested. They said battery good and was 99% charged! I don't understand why it would not turn engine just 30 minutes earlier, that 8 minute charge could not have fully charged it? When I replaced battery, I turned engine on and loosened positive battery post and pulled the connection, the car kept running. I thought it may have been alternator, but it should have died when I pulled positive connector. My girl did state, the whole time driving to work after the jump start, engine light was on. After i put battery in light went off. Any ideas?

My car has 90000 miles.
My car has an automatic transmission.