One just wont work, the other keeps flashing the apple logo

I have two 3rd gen ipods. One is dead. It won't charge, nothing. I connect it to my mac, it does nothing. Black screen all the time. Garbage? The second, gives me the apple logo to start up when connected to a power source, then dies, then goes to the start up logo, then dies...repeat! Is it also time to let that one go? I'm so sad :(