I'm 98% positive that the thottle in a Jeep Liberty is electronic, so probably the pedal isn't really connected to the throttle body. With this in mind, given your assestment on the behavior and the click your daughter heard, I would do the next:
- Check the pedals, check that the connections are properlly set. Clean the metal contacts with a mild acid(vinegar might do, light coke is good too), then rinse with water and finally if you want to be extra that the contacts are really bonding use a 2000(or more) grit sandpaper a brush them lightly, so you can give it more surface to contact with, don't over do it.
- Then follow the cables if you can. See that all wires are in good shape.
- Now pop the hood and check the throttle body and the throttle actuator, maybe is getting stuck because of oldness. This is were I think you would find your gremlin.
An electronic Throttle works by sending a signal to the ECU, then It gets processed and if everything is OK, It should open the throttle body and give you full power. Some ecu's would let you turn on the engine but nerf the performance, other just sit there like a glorified paperweight.
This means that you could have one of two problems:
- Disconnection by heat: This again can be separated in Two. Mechanically means that on plug, or cable, is disconnecting due to heat expansion. Could be a bad plug(corroded) or even a cut off cable that in some position makes a connection. The other is electronic, meaning that some component is getting so hot that the conductiveness of the material is getting diminished. Get a hold a off volt-amp-ohm tester and check connections. Also check for shorts, if you have "pimp her ride" check the accesories like a stereo.
- You have some other flag in the ECU that makes it think that is not a good idea to move the car. This is way too broad, I know. But as you mentioned that the low oil light comming up when oil level is fine, then you have a sensor problem. Which usually works with a diaphragm, wich is Mechanical and in some situations sound like a "click" when it get bended. Even better try to replicate it.
All said, I'll be checking every connection from the pedal to Throttle body, and the sensors for Oil pressure and coolant. Cables are prone to breaking specially where it changes from flexible to rigid, like a plug or a bend. When packed, cables "get used to" the way they when connected. So it's easy to overlook that.
And my last tip, buy one off those OBDII dongles they come as cheap as 10 dolar to like a zillion, but any will do. OBDII it's a standard shared between cars/trucks/motorcycles manufacturers. You can get access to some data, statistics, error codes and some criptic messages in your cellphone with just an app. Which can lead to isolate the problem and troubleshoot electronics in aless-hard fashion, or not to get scamed by some questionable meachanic. Here they pullf off the old switch and bait, "Yup! We had to change your transmission, How'd like to pay?'" when they only changed a sensor.
