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When you turn the key, is it a rapid clicking noise, or a 1-click per key turn?
what is the easiest way to clean the posts?
Believe it or not- baking soda and water, and a toothbrush!
Yep. Sounds even more like a battery issue. Sounds like it was "on its way out" 2 days ago, and has finally given up. Without putting a meter on it, i'd guess dead cell in the battery. After the battery replacement, might be a good idea to have the alternator checked to make sure that is not the root of the battery draining. Most local parts stores do this for Free in the parking lot, if you don't have access to a volt meter.