Car died and got a jump and car started /

Using the key FOB, turn off the alarm/unlock once the jumper cables are attached and then try to start.

I would say change the alternator out. Start with the simplest and cheapest factor first. Without the alternator keeping the engine running its hard to put it any gear.

Have the fault codes read. Replace faulty items. Use only genuine items as non-genuine replacement are not always compatible with the OEM fitted CPU units If you needed a bigger battery then the autozone salesperson should have sold you the correct battery first time round.( try getting a refund on the first battery) Jump starting an efi vehicle incorrectly will do serious damage to the control module requiring a new ecu unit. Check what is staying on when you switch off including interior lights/ boot light

Check all fuses ,wiring anywhere short or check alternatour

Did you get fuel recently, might have something in fuel e.g water? or even the fuel filter getting clogged.

I would try to jump it to see if the starter engages and the engine runs, if it does you have a connection problem between the engine starter and the battery, if it does the same thing with cables then you will probably have to tow it in to the shop. I do not think your problem is related to cold weather, but it could very well be related to the check engine light. Exactly what the check engine light is on for I can not say with out a code, but I agree with your thinking about taking it to the shop. Hope this helps, let me know.

HI there
Try checking a few things first like jump start again and then take off the earth lead only{black} and let it run for 6 minute on idle then turn on the head lights main beam ,,if the engine dies in about 2 minutes then the Alternator isent working full power as it should be pumping out 13.5 volts min and the lights should be bright and stay on... if not you have a Alt problem still like a bad feed to alternator or a bad connection on the battery post or a loose wire from engine to body {earth wire } also check out the relay to Alt ..
Let me know how you get on . RON

ignitor

this sounds like crankshaft position sensor, my Cherokee was ding same thing it ended up being crank shaft position sensor. this part costs about $50 and is easy to install.

might want to check the altinator i had the same problem last year repalce the battery and still had the problem after a few days turns out the altinator was not giving enough while in the drive postion butwould be ok in park