Check for spark, fuel delivery, and compression. This will narrow your list of possible problems.
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My car starts and runs fine .Yours may need a fuel filter or pump.
It could possibly be the timing belt. Chevrolet recommends replacing it every 60,000 miles.
Call the person who repaired the car and tell them what is going on. But what you write above makes no sense. You say, "(wont turn over) (wants to start) by (wont stay running)" If it won't turn over, how does it want to start, and how can it be running in the first place? Did they replace the fuel filter. If not, they should have.
lack of fuel
check ignition
Sounds like a plugged catalitic converter. When they heat up they block air from getting by and the engine will not run.
put gas in it!
It could be because its running out of battery
Make sure the Car is in PARK, if it is in gear like Drive or Reverse, the Car won't start even if the battery and starter are fine.
car start and drives fine bu when its turned off it wont start until it cools?
you can but it wont stay running if the battery is dead
dirty carb bowl or water in the carb