How to resolve charging and Bluetooth connection issues with new AirPods Pro?

I have a brand new pair of AirPod Pros that I won at a white elephant. Fresh out of the package.

one AirPod charges in the case, but never shows the symbol that it is charging and won’t connect to Bluetooth. The other AirPod says it is charging always, even when out of the case, but will connect to Bluetooth. I keep trying to do the factory reset, but because both the AirPods won’t connect to the case and say they are charging, then it doesn’t work. I’ve tried cleaning them and charging them all the way, turning on and off Bluetooth, forgetting and reconnecting them to my phone. Nothing is working. How do I fix this?

[Re-Titled by Moderator]

Original Title: Connection Issues