1997 taurus, start the engine, drive 5 min or 5 hrs. when i turn the car off and open the door the bell starts and dings for hours sometimes longer. please help me silence this.

Get a wiring diagram and check for power on all the power wires at the ignition switch. This is a known problem

You did not give the year and model, but generally I would start with the key switch. The switch controls everything you mentioned.

check the switch

one of the door ajar switches are sticking. needs to be put on the computer to find out which one. only other way is to go around and unplug the switches until your light shuts off.

there is a switch on the door frame the door hits this and brakes the turns the light and door chime off, will need cleaning or replacing.

1. flush the cooling system and replace your thermostat then check for oil leaks thats what you are smelling is burning oil

Where exactly does it sound like it's comeing from?
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You are probably unaware that your jeep has an aftermarket keyless entry system....Try this....roll down the drivers window....push the power door lock......get out/close the door...and attempt to open the door as u normally would.......it should be locked...... use your key to unlock the door....get in.....insert the key into the ignition and turn it to on...((((DON"T TRY 2 START IT UN TILL THE WARNING BELL STOPS DINGING & ALL THE DASH WARNING LIGHTS ARE OUT)))...........usually 5 dinging sounds.......at any rate just wait untill the sounds stops and fire up your jeep.....i hope this works for ya.....good luck

the lights are most likely the third brake light on the decklid... small line of led brake lights small unit.. i would clean the ignition switch with some quick start and cycle the key in and out to clean up the contact on the bottom some times soda or coffe gets in there and makes the car think that the cars key is in the ignition

Try replacing the ignition wiring harness in the steering column. These wires control I think everything electrical. I did and it fixed my problems.