WARNING: This page is about a different car, the 2003 GMC Safari and 2003 Chevrolet Astro. However, it is still accessible from the selected car via links, so may be relevant.
Refer to illustrations for STARTER SOLENOID DOES NOT CLICK symptom test. See Fig 1-Fig 3
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Fig 1: Starter Solenoid Does Not Click Symptom Test (1 Of 3)
Courtesy of GENERAL MOTORS CORP.
Fig 2: Starter Solenoid Does Not Click Symptom Test (2 Of 3)
Courtesy of GENERAL MOTORS CORP.
Fig 3: Starter Solenoid Does Not Click Symptom Test (3 Of 3)