I'd say it's probably "fried." Usually putting them through the wash ruins the logic board of the iPod, and it's almost definitely not worth replacing on the shuffle, i'd just invest in a new one.
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Well you could try fixing it, iFixit.com does have a teardown instructions here: [guide|1166] for you to follow if you do try.
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The part that's probably bad would be the logic board, but i'm not sure where you could buy one of those.
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You could try to see if apple would replace it, but usually when it's water damage they'll know and won't cover it. It certainly can't hurt to try, Apple replaces the oddest problems sometimes!
I'd say it's probably "fried." Usually putting them through the wash ruins the logic board of the iPod, and it's almost definitely not worth replacing on the shuffle, i'd just invest in a new one.