I don't know where your porblem really is but here are a few suggestions.
Cheap jumper cables are often useless. I have often had cars towed in that the owner could not start with jumpers but started immediately for us.
New batteries are often not well charged. It may help to charge the new battery fully. Even if it was well charged when it was installed, it needs a thorough charge after you found it dead. Driving the car for a while is not enough. A 2 amp trickle charge overnight is often what is needed if the battery was flat.
I would guess that you likely have a battery draw. Sometihing is not turning off or is shorted. After you get the battery fully checked out and fully charged if it keeps going dead, you will probably need professional help to track down what is acting up.
