Your Xbox 360 disc tray may get stuck in the open position from time to time. Here are some steps to try if it’s stuck open and the eject button won’t close it.
1. If the eject button works and it tries to close, but opens again once it gets close to the faceplate, check to make sure your faceplate is pushed all the way in. Push the faceplate in on all sides to make sure it’s fully clicked in and try the eject button again.
2. If you push the eject button and it sounds like it tries to move but won’t, then the tray could be off track slightly. Take both hands on the front of the tray and try to move it just slightly left to right, and up and down to see if you can get it back on track.
3. Try to push the tray in manually by pushing gently on the front of the tray until the front of the tray is flush with the faceplate. Once the tray is all the way in, try the eject button to see if it will open again.
If it continues to stay stuck in the open or closed position, you’ll probably want to submit a repair request through the Xbox 360 support site.