My 2004 jeep liberty stopped running two fridays ago. my mother was driving it, went into her insurance place and left my 13 y/o son in the car with the car running and a/c on. about 8 minutes into that the vehicle stopped running. He turned the key and thought some cold air was coming out. My mother came out a minute later and started the car. About 1 mile later it just stopped running. It will not crank all the way. Key turns, lights come on, but the fluids light stays on as well as the check engine light.Can anyone hel?

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Not likly but possible. Cat Converters usually only play up after some contamination causes blockage and usually only affects high rev range

So what is the question ?

You can not use it like that

You know how to diagnose &
repair yourself or you go to
a repair shop

it's overheating, for sure,
is coolant levels dropping? cold checked at rad cap?
"pulled over and found a hose to cool the radiator and hose near the thermostat,"
i can not understand this statement"above"
if it overheat only parked, check fan for full ops.
if overheats moving too, wont stay cool moving fast
then:
bad rad cap
bad thermostat , they have 7 year life says STANT. (and why)
belts slipping (to water pump)
rad cores blocked (IR thermo gun it) ask
water pump impellers rust 1/2 gone?

all this assumes no coolant loss, if you have loss, tell where.,
where it leans
ground
passengers toes (foot well)
engine oil pan? milky oil
if A/T TRANS, check it for milky too.

Any vehicle can be run without a key. Most times it will be obvious that tampering has taken place. If you can put a screwdriver into the key slot and are able to turn the lock, the lock was defeated. In fact, unless the lock was defeated, the vehicle's steering lock would preclude being able to actually drive the vehicle. If everything is intact, it sounds like the owner was looking to cash in on insurance.

NO, it is not safe to drive a a vehicle with accelerator problems. I will say for you to have this issue with a Jeep Liberty is very unusual.

HAVE IT SCAN TO CHECK FOR IDLE AIR CONTROL CODES.IF IDLE AIR CONTROL IS OKAY.YOU COULD HAVE BAD SPARK PLUGS AND WIRES.A LEAKING INTAKE GASKET OR MISSING VACUUM HOSES OR LINES AND A FAULTY FUEL INJECTOR WILL CAUSE CAR TO SHUT OFF WHILE COMING TO A STOP.

check the drive line play at the output of the transfer case to the rear universal joint.the gears are known for that.

I would check for leaks. After the car sits overnight look undernieth the cor on the drivers side. You are most likely going to see a tiny puddle of very thin oil. Check the tubing connections at the pump (mounted to the engine on the drivers side) and the front axel. Be certain to use Mopar power steering fluid when topping off. You may also need to get any air out of the system. Jack up the car so that both wheels are off the ground. With the engine turned off, turn the wheels to left and right lock positions a couple times. Lower the car, top off the fluid if necessary & give it a drive. Hope that works for ya.

It has a bad cooling fan relay. It isn't too easy to replace and it takes approx. 2 hrs to replace. It is located right behind pass or driver side headlight. It is flat and has 4 wires coming out of it. Hope this helps.