If the green light doesn't come on or only comes on when the cable is in a certain position, this usually means that the USB power wire is separated or cut somewhere between the USB plug itself and the circuit board in the amplifier. The x11 is notorious for this and other wire-related problems as they were designed for flexibility and convenience but not total reliability.

If you're not moderately experienced with splicing, soldering and electrical troubleshooting, I recommend cutting your losses and getting a replacement. Check your warranty/return information for an easy way out, else sell whats left on ebay and drop a dime on a newer/better headset.

However, if you have dealt with a few patch jobs in the past, start with looking for obvious spots on the wire. Cut, strip and splice as needed. There are 4 insulated wires and the shielding/power. If this is a no-go, remove the housing of the amplifier and double-check the solder points for good contact.

The last two spots to check are a little tougher to get to, the splitter near the USB plug and the USB plug itself. Cut open the USB plug and check contacts. Replace pins or solder as needed. If the problem is in the splitter, handle similarly to a splice in the wire but make sure you are careful with all of the other wires to not damage them in the process.

Good luck if you haven't already given up on it!