Possibly received bad battery...
I just replaced the battery in an ipod video with a new one provided by you. The repair went smoothly - I've done this before with other ipods using your fine replacement materials and instructions . It works fine when I plug it in to charge - all the music is available and plays without a problem. As soon as I disconnect the charger, however, the ipod goes dead and cannot be booted. If I leave it on the charger, the little icon comes on saying that it is charging, but even after many hours, it does not charge.
You can try a new battery but first, I would make sure that the cable for the battery is connected to the logic board correctly. Lift up the connector to the batter flex cable, then remove the cable. Make sure the contacts are facing the correct direction. Use this guide to help: iPod 5th Generation (Video) Battery Replacement Make sure the brown clip for the battery's cable is pressed down all the way. Once you have tried this, see if the battery will allow the iPod to turn on. If it doesn't, you may have a bad battery or have damaged the battery connector on the iPod's logic board. That is the little brown connector that the cable goes into. Let me know in a comment if you need any other help. I have been working on these for a very long time. :)
bcohan, my first instinct would be to say yes. Now I do know that the 5th gen has had issues with the charging circuit and some coil problems. I suppose for the few dollars for a replacement battery, I'd go that way first. If you still have problems after that, you may have to take a closer look at the logic board. Good Luck