Why won't my iPod get past the boot screen?

A few days ago I was on my iPod and it shut off automatically. Upon turning it back on, it displayed the boot screen (apple logo) for 10-20 seconds then shut off. It still continues to do this. I ready a few places online about putting it in restore mode and so forth. I was able to get it in DFU mode and I reverted back to an older firmware. I got the loading screen on my iPod that you aways get when updating it. When it was done, Itunes said it was successfully restored and was now rebooting. Upon rebooting, same thing. It just shuts off. I've left it on a charge for a good period of time so I know its not just a dead battery. Basically I need to know if and what I can do to fix it or if it is time to chunk it and get a new one.