No, the remote control does not have a battery. You can try cleaning the metal contacts on the connector with a q-tip and rubbing alcohol.
If it still doesn’t work, you may be able to find a replacement - but be careful, some of them have a different connector that doesn’t work with the 2nd generation iPod, even ones that are listed as working for the 2nd generation. Make sure that that the connector is the same as the one you have.
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