My new AirPods case is not working

You can try this first:

How to reset your AirPods and AirPods Pro - Apple Support

If they are brand new, don't fool around with them anymore than that. See if you can return or exchange them:

Returns & Refunds - Shopping Help - Apple

Gromoll Said:

"My new AirPods case is not working: My AirPods case is not charging, the light does not come on and it is not connected to my devices."

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Refer to the link atop this thread.