I have to jump on board here with similar issues.
I can use the Corsair Wireless plugged in via USB. Audio, Headphones are awesome. I have updated the firmware to the latest 38.01, I have even tried forcing firmware update to 38.01 again. After the update the headset blinks red to indicate charging then after a while it blinks different colours. Then I thought hey it's charged.
As soon as I unplug the device from the USB, it doesn't turn on. then it doesn't go back to charging either. I can force firmware again then it starts charging and blinking red.
Is there another firmware I can test? Or do I have a faulty headset that needs returning? Just bought it few days ago. I purchased the wireless version thinking not having to have wires would be pretty convenient.