Had the same exact problem on my 2000 Sable. Checked ignition switch. Good. Replaced battery. No change. Replace starter. No change. Starter solenoid engaging when ignition turned on. What it ended up being was an $8 positive wiring cable coming directly from the battery to the starter. Even though it checked good with an ohmmeter.(good continuity) Under load, it became an open circuit. Thus, the 12vdc could not transfer to the starter motor. Save yourself hundreds of dollars and time with an $8 dollar cable.
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Had the same exact problem on my 2000 Sable. Checked ignition switch. Good. Replaced battery. No change. Replace starter. No change. Starter solenoid engaging when ignition turned on. What it ended up being was an $8 positive wiring cable coming directly from the battery to the starter. Even though it checked good with an ohmmeter.(good continuity) Under load, it became an open circuit. Thus, the 12vdc could not transfer to the starter motor. Save yourself hundreds of dollars and time with an $8 dollar cable.