Sounds like a draw somewhere as mentioned above.

If your battery is completely dead, a jump start may not work even with the best cables. The current is trying to charge the dead battery and there isn't enough left to crank the starter. Either charge the battery or let the other car connected with cables run (15 -30 minutes) for a while to give the dead battery some life. Your best to get a battery charger - your alternator is designed to keep a battery charged, not recharge it from a dead state. It will work but put your alternator to its fullest output only to shorten its life.

It could be a defective battery, but doubtful.

James