hi new here ; my stepdaughter ask me to check her car out . here,s the problem it starts with a jumpstart and runs fine , but turn it off wont start what do you think it is ?

My first guess would be a bad battery connection at the terminals, or a battery that has failed, i.e. had an internal crack in the connection between its 6 cells or was just old and 'sulphated': Or, in the event that the negative jumper cable was connected to the metal of the car, not to the negative terminal on the battery - that you had a corroded or loose ground cable, from battery to wherever that cable is bolted onto the motor. This location might be invisible with the inlet air duct in place, or it might be hidden under the battery and its support tray.
When you try to start it by itself: 1. does the engine crank over at all, and fast or slowly? 2. do the indicators lights in the instrument cluster (the SES light, the seat belt light, alternator light, etc.) come on when you turn the ignition key on, but before you try to start the car?
If it the engine cranks over merrily over but still wont start, then I dont know what the problem is. These cars had a 'security system' that would prevent the engine from starting in the event the doors had been locked with the 'dongle', and you then opened the doors with the key instead of unlocking using the dongle (the horn would being honking), and tried to start it. The owners manuals described the procedure for getting around this, but of course it didnt explain what would happen if/when that security system went senile.
A way to check the health of the battery and electrical system, is to open the drivers door so the domelight is on. See how bright it is. Put in the ignition key and turn the ignition on, then turn on the headlights. The dome light should be just about the same brightness - though you will be able to tell it dimmed very slightly. If the light gets really dim - its a problem either with a discharged battery, a bad connection somewhere (the negative/ground cables are just as important as the positive cables) or a battery having an internal problem.
If you have a voltmeter you can check the battery voltage. It should be about 12.6 volts when the battery is charged but the engine is off, and has been off for 10 or 15 minutes. With the engine running it should be above 13 volts, and closer to 14 volts after its been running for half an hour or more. With a charged battery in good shape, it should only drop to about 11.2 or 11.5 with the headlights on - and the motor not running.
Its possible the battery connections just need to be 'rotated' a little and retightened. It takes an 8 mm wrench, or 5/16ths" wrench, and (preferrably a 6 point, not a 12 point type) to loosen and retighten those side-terminal bolts, and you -AlwayS- loosen and disconnect the negative cable first; before you put a wrench on the positive cable bolt - to avoid shorting from your wrench to any metal nearby.

hi new here ; my stepdaughter ask me to check her car out . here,s the problem it starts with a jumpstart and runs fine , but turn it off wont start what do you think it is ?

does it crank on its own?

NO : Check battery connections. the fact it starts when its jumps says the starter is fine. Clean the batter connections of any corrosion. You want them sparkly clean. Still no start? Bring the battery to Advanced auto /autozone and have them check the battery.

Yes: is there spark at the coil towers? if theres no spark, the the likely suspect is the Crankshaft Position Sensor.

The security system prevents the car from even cranking. However since you can jump start the car, the security system is not the problem.

Im leaning towards bad battery or bad connections.