if the car dies after the jumper pack is disconnected its gonna be a bit hard to drive it somewhere lol.
option 1: ring anytime-towing for $100 and get it towed to a workshop.
option 2: check the charge rate while its running off the jumper pack, this should point u towards either alternator or battery
option 3: buy a new battery. Dont buy the cheapest battery from supershit either, just a normal heavy duty with caps that you can top up with water. Dont get a maintenance free battery as if you do have charging issues it wont do the battery any favours being constantly flat and recharged. If its not the battery at least you'll have a new one which'll make diagnosing easier.
btw your charger sounds fked, for anyone wanting to buy a battery charger i recommend a CTEK charger i got the 8amp one and it does everything and will fully charge a massive battery in under a day, can also leave it on charge for months without doing any harm.