Car completely shuts down and acts like battery is dead

When you jump start are you putting earth to the body/chassis or to the battery??

The battery could still need replacing. It just depends on how old it is. Some batteries last 3 years if you are lucky.

have a load test done on the battery as there is a dead cell evident.

you mentioned new alternator and battery, but it seem that the alternator is not charging, when you install the new battery the car started and run and after hours of running specially if head light is on the car shuts down. this is an indication that the alternator is not charging. (factory defect) have it checked or return part to auto supply.
if alternator is good and you have the car jumped and run it will not shut down even if your battery is dead because the charge of the alternator is enough to power the electrical system of the car until you turn it off. this applies to all cars

I suspect that the battery is dead and when you turned on the lights there is insufficient current from the alternator to run everything so the ignition shut down. Have a load test done on the battery and check for bad cells as a battery sitting unused for 2 years will be sulphated up on the plates.. Fit new battery and reset the CPU with a code reader.

it jumped time needs new timeing belt and put back in time. to check pull front of moter down and check.

yes replace battery the computer cant work on a dead battery ..

Battery is dead... get a volt meter, jump the car and with the car running on its own power check the voltage, anything less than 12v could point to an alternator but a new battery is a better place to start. put it to you this way if the car shuts off while driving, then its your alt, and if its fine wen drivin but wont start back up... its all battery

Can also be corrosion in the inside of you batt cables,also check your battery to see if its holding an charge,allot of auto parts stores will check this for free.

Always clean the battery terminals before jumping. An extremely dead battery may not accept a jump as it serves as a 'buffer" instead of helping. If you do get it started, charge battery with a battery charger then have alternator and battery tested for proper operation and check belt condition and tension as well.