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hello what state of charge is the 12 volt battery now? do you have a voltmeter? If it starts with a jump start and all the lights go off it may need a new 12 volt battery.
That's because most troubleshooting requires specialized equipment and a professional that knows what they are doing, these cars are somewhat complicated and have about 20 plus computer systems related to the hybrid system, the only thing you can do yourself is what I already mentioned to you, check the 12 volt battery, if it starts and runs with a jump it needs this battery which is in the trunk, the reason it dies out when disconnecting the jumper is because there is no alternator, the battery takes about 5 hours to charge back up, you may consider using a trickle charger set at about 10 amps for about 5 hours and if it doesn't charge sufficiently to operate the computers try replacing the battery.