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Does anything electrical work like the dome light and so on when you tried jump starting the car?

when you step on the brake pedal, do you see the brake lights coming on?

Well the only thing I have seen that can cause this is if you jumped the car backwards. That blows the IPDM and BCM, which can cause what your describing.

Are you 100% sure you jumped the car correctly?

Well if the key is not able to turn on, then advanced diagnostics need to be done. These push button start systems can be very tricky to figure out if they are not responding.

Like I said, normally when I have seen this happen, it's jumped backwards and the IPDM and BCM need to be replaced to resolve. Sometimes just the IPDM.

Try this for the heck of it.

Loosen the negative battery cable and wiggle it side to side and tighten it back up in a different position, then do the same for the positive.

Maybe it a poor battery connection.

The head lights are not as much of a load as the starting system.

Do you have another key you can try?

Maybe there is a problem with that key also?

These type of problems are really tough, and even tougher online.

Let me check to see if there is any thing is in the data base tomorrow at work. Then I will get back to you.