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This sounds like you may have a bad starter. Do you have a voltmeter so that we can be sure?
That does make it hard to test then. She can try to start it while in neutral and see if that helps.
If she can find someone to help her they can try taking a long pipe or bar and hammer and tap on the starter while she turns the key it may start. Other than that there is not much she can do.
This is an automatic I assume.
Yes there is a solenoid on the starter. I am not sure if AAA will want to apply 12 volts right to the solenoid which would bypass the starter relay. I hardly ever see a starter relay go bad.
With the age of your CR-V chances are better that it is the starter.
Yes that price is about right. I am in Illinois and just quoted an Odyssey starter and it was almost $600.00