iPod got wet: works but screen usually doesn't come on

Yes, I did it, I got my iPod wet. It was in water for about 10 seconds I believe. I switched the screen on (another mistake, I know) a couple times to see if it worked but it kept going straight off again. So I left it in rice for a week (all praise the rice), and now it works perfectly (shows up in iTunes etc etc) but the screen never comes on - except for one time, when it was working fine for about half an hour then the screen just went again.

Is there anyhting I can do? How much would repairs be? I've since bought a Google Nexus 4 so I'm not too bothered and wouldn't want to spend too much.