Wanted to be helpful.
Don't throw away your camera. If you have cleaned the contacts and plugged it in and you get no blinking white light then you are not charging.
If your camera will not charge, try setting the mounting setting in the Camera Settings for that specific camera in your Google Home App. Make sure it is the one set for the magnetic mount.
Specifically: Under "Device Information" (for the camera you are trying to charge) ensure the "Camera Mount" setting is set to "Made for Google or Google Nest mount".
Thanks for posting and we appreciate your time in providing the Community the steps that fix the charging issues of the Nest Camera (battery) — it's a big help. Feel free to respond to this thread if you have additional questions or concerns and I'd be glad to answer it for you.