Is it turning on at all when plugged in? If they have a flat battery, they usually turn on a couple of minutes after being plugged in. I have a Touch like that. One problem is that it doesn't update the firmware or books as it can't run when not plugged in.
And, it is worthwhile to just leave it plugged in for a day or so. There have been lots of reports of devices not powering on, but, suddenly come to life after a day on charge.
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