dead battery, car won’t start

I have a 1990 honda prelude with a lot of extras, I have an remote start/alarm, 2 amps at about 100 watts RMS eash ,lcd in dash monitor,150 watt power inverter(dc to ac), underbody light kit,2 sets of fog lights and 10  led light through out the car and i moved the battery in the trunk .

I have a problem with my  battery dying, I "m not sure what the cause is. when i jump start my car it starts right up, but if i turn it right off and try to start it with out the jumper cabels it still won't start. if i drive it around for a while it will start back up for like an hour after i drive it but any longer and it dies.   So i though it was the battery and bought a new duralast gold battery it lasted for like a week and a half and then it went dead. My little honda only alternators only like 70 amps , if my add-on electronics draw more amps than the alternator produces would that cause the battery not to charge fully ? or would the dead battery be because of a draw when the car is turned off? and how would i fix it , buy a new or second battery ? new alternator? I'm sick of jump starting  my car