My son's Nintendo DS won;t stay on.

My son's blue Nintendp DS is not working right. It will turn on, and the battery says it is fully charged. But whenever my son turns it on, it says on for about 30 seconds and then the screen flashes white for a second then shuts off. In 2012, the DS got wet in a storm, but after that in 2013 it worked fine. But in 2014 it had this "Turning on problem.", and hasn't worked since. My son's DS is blue and is about 5-6 years old. My son had a lot of fun with it, but now he really wants to get it fixed or get a new one. Could you please tell me how to fix it?