Test the fuel system pressure. The fuel pressure should read within specifications for the engine in your Cavalier, either the 2.2L engine or the 2.4L engine. Correct fuel pump pressure specifications and more are in your ChiltonDIY subscription for your 2002 Chevrolet Cavalier.
Luis, it could be a faulty fuel pump, or a faulty idle air control (IAC) valve.
First, have the battery charged and load tested. Once your battery is fully charged, try starting your Taurus.
Test the fuel pressure with the vacuum hose connected at the regulator. Your fuel pressure should read within the specifications. Follow this PATH: Engine Mechanical > Specifications > Gasoline Engine Tune-Up Specifications in your ChiltonDIY subscription for the correct specifications.
Inspect the fuel pressure regulator and don’t forget to check the fuel filter!
With a scan tool check for history codes (diagnostic trouble codes or DTCs).
Review the coolant temperature readings and the IAC duty cycle.
The IAC valve adjusts the engine idle speed. The valve is located on the side of the throttle body. The valve is controlled by a duty cycle signal from the PCM and allows air to bypass the throttle plate in order to maintain the proper idle speed. Do not attempt to clean the IAC valve. Carburetor tune-up cleaners or any type of solvent cleaners will damage the internal components of the valve.
There is a technical service bulletin (TSB) that may apply. In your Chilton subscription for the 2002 Taurus, go to “TSBs” and then filter by symptom. Choose the symptom: “Engine stalls.”
It could be a faulty fuel pump, check the fuel pressure to make sure it is within specification. From the navigation tree, find the specification for the 2.2L engine in your ChiltonDIY by following this PATH: Engine Mechanical > Specifications > Gasoline Engine Tune-Up Specifications.
It very well could be the fuel pump. I would scan for diagnostic trouble codes (DTCs), Look for DTC P0171 and P0172, which may be associated with a fuel supply problem.
Has the fuel filter been serviced lately?
Check the fuel system pressure, the correct specification for your 2001 SC1 Saturn Coupe is in your ChiltonDIY subscription, follow this PATH: Diagnostics > Diagnostic Routines > Powertrain > Engine Controls – 1.9L > Fuel System Diagnosis.
Check the battery voltage, the minimum is 12 volts.