You say it works with external power, correct? Does it work correctly - able to play music and so on? If so, it's probably just the battery that's damaged. Unfortunately as you can see in the repair guides here, its tricky to open up.
I had similar trouble once - after I sent my "Stick of Gum" iPod Shuffle through the wash at the laundromat. It managed to get suck between the dryer's drum and door, grinding a gash almost all the way through the case and utterly destroying the buttons. Incredibly, it survived and continued to work! Of course, it only worked with external power. It turns out that although the circuitry was a-ok, the battery was shot - and after removing the battery, it worked for a year afterwards as a perfectly good USB flash drive.
One other thing you might try - as suggested by mayer - is to open it up and carefully clean the inside if you spot residue. Years ago, I managed to resurrect my Gameboy Pocket this way after a similar encounter with a grape slushy...