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I realize i will not be able to use the iPod without the battery, but will the hard drive (or flash drive in the nanos case, right?) still retain its memory while NOT plugged into a power source? Will it connect to the computer at all with out a battery?

Yes, you can use it as a flash drive as the memory is a non-volatile NAND flash (basically means, when its off, it’ll still retain data) I had a 1st gen iPod shuffle with a dead battery, which I took out, and it still works as a flash drive! (It was shaped like one too…)