I will definitely ask them about the ground connection next time I speak to the garage, thanks.

Both times the car was already warmed up. Has happened when I was running errands. After getting back in the car to restart, the car was dead, completely. No dash lights, no radio, key fob doesn't work. The whole system is down. No clicking when trying to restart, just dead silence.

The car stalled out once at a light, but I think it may have been from jumping it too many times?