My iPod Touch 2nd generation is dead
It sounds like there a good possibility of it being a hardware issue, in which case you should contact Apple. 

If you haven't already, about the only thing to do, is plug it into your computer for about 15 minutes. Sometimes it takes awhile, if the battery is completely dead, to get the charge started. But, I'm pretty confident that won't work, considering it had life before you plugged it in. It would be something to try if you wanted to take the time.