1996 ES300 starts and dies

Hello,
I have a 1996 Lexus ES300 that is dead in a parking lot. The battery is completely dead... I can jump it with our other car and it starts
and runs, but as soon as put it in gear I start driving the ABS light comes on and it dies shortly thereafter. Then it will not start unless I jump it again.
Is this a bad alternator? I wonder because it runs until I start driving, I would think with a bad alternator it would die even in Park.
Any help is appreciated. Thanks in advance!
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Check to make sure the battery clamps are tight around the battery posts. After you start the car, run the engine at about 1,500 to 2,000 RPM for a few minutes before putting it in park. When was the last time the car was serviced, i.e., spark plugs and air filter replaced, etc.?
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Ray O
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