My LC (Pizza box) does this from time to time. It went away when I pulled the speaker and cleaned the contact feet for it on the Motherboard. I am not sure what the internals of the Classic look like, but if it has a similar setup, it may just be a dusty / oxidized connection.
Use some Alcohol based cleaner, and you should be set! If not, plug a pair of headphones (or something else) into the Headphone / speaker jack in the back of the computer. That should turn off the circuitry for the internal speaker and bypass this problem.
HTH
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