Your Xbox 360 disc tray may get stuck in the closed position from time to time. Here are some steps to try if it’s stuck shut and the eject button won’t open it.
1. Try to remove the faceplate and hit the eject button again to see if the faceplate is blocking the tray somehow. If the faceplate is what’s blocking the tray from opening, you may need to purchase a new faceplate.
2. Try to eject the tray manually.
a. On the original Xbox 360, there is a tiny eject hole behind the face plate right beneath the X in Xbox 360 written on the tray. Push a paper clip into this hole about an inch until you feel pressure, then push slightly and it should pop the tray open.
b. On the newer Xbox 360 S, there is a tiny eject hole on the left side of the console behind the vent when it’s laying flat. If you lay it flat and look on the left side close to the front, you should see a yellow sticker behind the vent and a tiny hole. Push a paper clip into this hole about an inch until you feel pressure, then push slightly and it should pop the tray open.
If it continues to stick, you’ll probably want to submit a repair request through the Xbox 360 support site.