Check voltages...
With
intermittent problems, you need to be able to "see" what is happening when the problem occurs.
What can happen is there can be a loose connection. You can have a very good battery, but the loose connections makes the electricity downstream from that bad connect like you have a bad battery!
And electronic gizmos like the computer which controls the engine will not function under around 9 volts.
So you could have a good battery, bad connection, battery drops to 10 volts when starting, but beyond the bad connection, voltage it drops to 7 or 8 volts and the engine computer will not work - it will not start. Then you jump the battery and then maybe up the starting voltage to 11 volts when starting (just guessing), and also up the downstream from bad connection up a few volts to maybe 9 volts, then the electronics work and the engine starts.
So with that said, we need to monitor what is going on as this problem occurs.
Let's use some test leads, wire, an open window, and a volt meter...
Test leads...
So connect the test leads to the battery and to two wires you run through your open window, then connect these to a volt meter.
Now you can see the voltage of the battery as you start the vehicle. It should be 12 something volts with just the ignition on (not starting). Then drop to around 10 volts when starting.
If it drops below 9 volts when starting, charge the battery with a battery charger and try again. Try jump starting and see what the voltages are.
If you charge the battery and it still drops below 9 volts, replace the battery.
But if the battery is good and is measuring 10 volts when starting, move the test wires down the line. Maybe tap into the cigarette lighter. See what the voltage is reading inside the vehicle.
If there is a big difference inside the vehicle from what the battery is reading, then there is a bad connection somewhere.
Test various spots in the + positive wires between the cigarette lighter and the battery. And test various negative locations. (Move the test leads around.)
Don't forget the main ground wire to the engine block.
Check on one side of a connector, then check on the other side.
More on this and other testing methods...
http://www.engine-light-help.com/voltage-drop.html