what do you mean it won't turn on it happened to me I powered off my iPod completely and when I tried booting it up it stayed at the Apple logo for several minutes before just turning off again. Apple guys said it was because of 3.1.3. ended up restoring.
Your not providing much to go on. Are you saying that it's fully charged and it is hot? Let it cool down. If your saying it heats up when charging and shuts down, if letting it cool does not help, it may be a hardware issue. You didn't spill your drink on it too did you?
I called Apple Care and i must say, they are so nice. They listened to me! And only kept me on wait for 3 minutes! THEY ARE AMAZING! So I'll be iPod-less for a week. - It will be shipped to California.
Have to agree with Random_Guy on this one. In my personal experience, Microsoft actually has the best customer service. (In my personal experience, that is)