Instructions
Manual Solution
Press the power button on the Xbox 360. Depress and hold down the eject button on the front of the console. Wait a few moments and see if the tray successfully opens.
Tap the side and the top of the console firmly two or three times. Sometimes, wires inside the console can become loose, causing the disc tray to become unresponsive. Tapping the console firmly can put the wires back into place.
Insert a straightened paperclip into the hole beneath the right-hand side of the Xbox 360 disc tray. This will force the tray to open. Check and see whether any sticky discs are in the tray to have caused the problem.
Repair Ticket
Navigate to the Microsoft website for Xbox 360 repair.
Click "Start a Repair Request."
Fill out the requested form, which includes your name, address and Xbox 360 serial number. The serial number is on the backside of the console. You will receive an email confirming your ticket, along with a region-specific address to which you must mail the console.
Remove all connected accessories. Microsoft only needs the bare console.
Find a local shipping facility (post office or specialty courier company) and ask about safely packing the console. Send it to the address you were given from Microsoft.