1998 Chrysler Concorde just stopped running while driving down the road. No warnings, the engine just shut down. The check engine light did not come on, the lights stayed on. When I tried to restart it, it turned over but would not start. What could have caused this?

You have to fix the problem, not find a way to bypass it. The anti-theft system is designed to stop exactly what you are trying to do. Call out a mobile auto-locksmith.

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No generic code reader will read anything other than PCM/ECU codes, and sometimes ABS codes if you spend a little extra money.

The 1998 Chrysler Concorde also didn't have a instrument cluster that was controlled by the Body Computer. (BCM)
If your speedometer is working occasionally, then chances are that there is a intermittent short in the wiring or that one gauge is just going bad.

While you're driving or when it happens, try to pay attention to what makes it happen... Hitting bumps in the road or hitting the dash with your hand will be a sign of possible bad wiring.
If it worked when you shut the car off, and then doesn't work when you start it back up the next day could mean that the speedometer and/or instrument cluster is going bad.

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Try checking the electrical connection on top of the sender unit that houses the fuel pump

You have a check light on

What codes have you retrieved?

What testing has been done?

i would first check the crank position sensor,i have seen this many times before.

Three things make the engine run. Air, fuel, spark. One or more of those is not present and the engine stops.pull a plug wire off, put a screwdriver in the end, have a friend turn over the engine while u hold the screwdriver near a metal part of the engine(dont touch the wire or screwdriver) look to see if there is a blueish white spark. If no then u have to trouble shoot the ignition. if yes... take off the air filter, spray some starter fluid in the air entrance and try to start. If it starts u have a fuel problem.
If the car has high mileage the timing belt could have broke

1998 Chrysler Concorde just stopped running while driving down the road. No warnings, the engine just shut down. The check engine light did not come on, the lights stayed on. When I tried to restart it, it turned over but would not start. What could have caused this?

Have your transmission oil filter changed;
it is located under the transmission pan
The oil is what makes the transmission shift
When you shut off the engine it stops the transmission pump then when you start up again the transmission shifts until the filter clogs again

Could be the smaller wire at the battery terminal,clean battery terminals and check connections are tight.

sounds like a tipical crankshaft position sensor will fix your car