Have you tried different chargers and left the pen plugged in for a few minutes? If it is the pen in the picture, it does have a battery and should be rechargeable. Then it's probably just faulty if it won't charge, and you can open a case in your user account and get a new pen.

Hello,
Please check that it's a rechargeable model and not a battery model, as there are 2 models. The USB connector on the battery-powered model is used to download audio files, while that on the rechargeable model is used to charge the device and download audio files.

It's a pen with a battery.

The pens have batteries, press the light-coloured button with a biro to open them. AA batteries as far as I know