Chosen Solution
I replaced the battery in my iPod touch 4th gen. it only works when plugged in electricity. it does not work when plug it into computer.it keep rebooting when it is first plugged in.
mfrench1 sounds like you possibly have a bad battery. I would replace it once more. Even if your iPod is not charging or syncing due to a bad dock connector, it should at least still come on for a short while with the new battery.
This happened to my water damaged iPod. There was corrosion all over it so I opened it up and replaced the battery (this is a must not an option). then I soaked it in isopropyl alcohol for 15 minutes and scrubbed with a toothbrush. It works great now!
