Going through a washing machine cycle isn't the iPod getting "just a little bit wet" (which is sometimes rescued by placing the iPod in a bag of uncooked rice for up to a week), it's a full soaking, which is usually the end for the iPod.
Dry rice absorbs the moisture, taking it away from the iPod. However, after a cycle in the washing machine, the chances are that the power from the battery has caused a short circuit and burnt out some parts of the iPod. I suspect your iPod is not salvageable.