Camera doesn't want to turn on

I met this issue second time.

After few days of using new camera it suddenly stopped to respond with nearly full battery and didn't start after replacing battery for fully charged. But it started again when connected to charger. After disconnecting didn't react again. I've send camera back to store and got another one. After next few days problem appeared again.

Camera is working properly connected to charger only. After disconnecting charging led is slowly blinking and camera doesn't turn on. Charging led stop blinking after 10-15 minutes.

Any ideas?