The fact that the engine won't run with the jump pack disconnected and the flat car battery still connected tells me the car battery is knackered, totally and utterly, I wouldn't even waste my time or the electricity to charge it. It will have to be replaced. If you continually try to start it and try to disconnect the jump pack you will damage something, and it won't just be a fuse, most likely the alternator.
The alternator needs a 12V supply to regulate its field winding, to be able produce a charge. Normally this would be supplied by the car battery, but as yours is totally had it, when you disconnect the jump pack you lose the supply to the field winding alternator stops charging, and engine stops because there is no supply to the ECU, fuel pump, ignition system etc.
Have to disagree with the comment to using a trickle charge to try to recover a deeply discharged battery, I was always led to believe the plates in a battery become sulphated over time, and it needs a short very high initial charge in excess of 20-30A (industrial charger I,m afraid) to start with, this is to attempt to boil the said sulphate off of the plates, though you do run the risk of buckling the plates of the battery, then reduce it to a lower more sensible charging rate.
I expect the O/P's battery once connected to the charger will try to pull such a high current it will cut out through thermal trip, blow a fuse or the like.
