When the jump leads were connected from his van to my car, it took about 10-15 minutes of running continuous power to my car for it to start.

However, once he turned off his van's engine my car totally lost power and would not start off it's own power.

I did manage to drive to the garage, as he connected some sort of temporary power pack to my battery.

At the garage, when he disconnected it, the car was still running. Should I ask the garage to make sure it's the alternator that's the issue or is what I have described a classic alternator problem?