Suggestion:
sounds like you have something disconnected on your celica
reasoning – it takes the jumper car – to make the connection complete
and when that is removed – you lose it in the celica
battery may be bad – I would have that checked
and sometimes in an older car – when you replace the battery
you have to replace the alternator, too
may just have one wire disconnected – and where that is ???????
sorry – just experience – not an SAE mechanic
all the best

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sounds to me like your alternator needs new brushes in it's voltage regulator. plus the battery is probably completely dead.
The battery only STARTS the car–the alternator and the voltage regulator recharge the battery as it runs–and they provide the electrical power to keep the car running=–NOT the battery.. SO—the alternator OR the voltage regulator are probably bad. Go to a GOOD mechanic for a proper check AND repair.