Non-starting problem after using vehicle & turning off.
It appears you are willing to throw a few parts at it, and see.
Here is one to try.
There are 2 engine coolant temperature switches that screw into the block.
One controls the fan that cools the radiator in the front.
The other is hooked to the computer and tells it what your engine temperature is.
Specifically, it tells if the engine is cold or hot.
When this sensor fails, it will tell the computer that is engine is cold when it is not, and then the computer will make it so the engine will not start.
Sometimes these two sensors are even the same part number.
Try replacing that (computer) temperature sensor, it should be cheap.
God bless your efforts.
What causes a car not to crank when hot
This is a common symptom (if not the most common symptom) of a failing starter. It will crank when cold and will not crank when engine gets hot. This is a failing condition and eventually won't crank when it's cold either.
It's also possible but not nearly as likely that the timing of the motor is too far advanced. When the motor warms up, the timing advances further to a point where the motor is too difficult to crank.
How do I replace alternater brushs
You don't, usually if the brushes are worn to the point that they need replacement the slip rings that they are in contact with are worn through too, you are better to just replace the alternator.
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