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Are you experiencing a deep freeze where you are right now? Give this a try- turn the key to start, and hold it there- I know back in 2001 or so we had a bunch of these that would seem to get "frosty" in the cold, and not be able to make connection- but holding it there melted the frost in the terminals, and then it would suddenly crank after about 20 seconds.
if that doesn't do it, I would have the battery checked to make sure it is OK- not just 12v, but have it load tested to make sure the amperage flow is sufficient to crank an engine. any chain parts store will do this for FREE for you.
Are you sure the whine wasn't the starter spinning, but not throwing out to engage the flywheel?