Car won't start at all dash lights or turn signals don't work

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I have 244,000 miles on my Acura. Recently, I had a squeaking belt, I noticed a whining sound, and when I push in the clutch, sometimes the lights would dim and the car would almost stall. There is a lot of corrosion on the battery terminals. Car will not start at all. Do I have a big problem? I replaced the alternator in March of 2009.