Why is traction control and check engine light on in Chrysler 300

Possible failed abs sensor have scanned with a scanner with abs capibality

Your first option is to get the vehicle plugged into a diagnostic system or an OBD2 scanner to find the error codes. These will help get a more accurate idea of what is wrong.
The two warning lights seem to suggest two separate issues so the codes will help a lot. When you get the codes comment and I'll try to help translate them for you.

Check your wheel speed sensors first.

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PCM/TCM Software Updates Will Address Shifting Problems ...

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Chrysler 300 PCM/TCM Software Updates Will Address Shifting Problems. ... If you experience rough shift and/or shuddering during gear shifting, software ... Car would not go over 20 mph and check engine light along with ABS/BAP light ... Once he put the new battery in the car ran fine for a while and the problems all cam ...Missing: p

ECM with bad connection, causing engine to stall - 2005 ...

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Any time the check engine light comes on the traction control will be disabled and the light will also come on. Start with scanning the engine computer for trouble codes to see why the check engine light is on.

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Any time the check engine light comes on the traction control will be disabled and the light will also come on. Start with scanning the engine computer for trouble codes to see why the check engine light is on.

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

Engine light on means that your lambda probe is malfunctioning just raplace it and it will come off,or the mixture of gases and gas is not proper and you need to tune the car at bosch motronic.
traction control warning light means that the sensors analizing it are malfunctioning and or you have a serious problem on the traction control

The ABS sensor is a speed sensor also for Traction Control. This is why both lights are on , One of your front ABS sensors are bad or disconnected, or has a pinched wire.

vsc shuts down any time check engine light comes on. repair engine light problem, reset computer monitoring system and vsc light will go off. must scan computer to pull codes for check engine light and go from there.

there is nothing to do here but have the dealer run a scanner test to see what trouble codes were set with the lights coming on, until then there is no way to tell what the problem might be as there are over 200 possibilities.