My iPod Touch 4G has been going wonky on me lately. Help?

I will hit the lock button and see a battery low sign, I plug it in and it turns on. After 40-60 seconds, a white overlay apears(I can still see through the white at the screen I was looking at before) and then I get an Apple logo and it shuts off. My computer gets angry because the ipod has disappeared. Then, because it is still plugged in, it repeats the process.

I cannot keep it on long enough to sync or reset to factory. Holding the home and lock button to reset doesn't work; I get a snapshot and then the VoiceControl screen appears. Turning it off then on doesn't help. This iPod has my life in its tiny little memory. Help??

Also, as far as I can tell, it isn't holding the charge it should be getting from being plugged in.