The gears on the Xbox 360 have become misaligned. Here is how you fix it. If the tray is out all the way disconnect the power.
Step 1:
Locate the tab on the left side of the tray.
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Step 2:
Lift the tab with a pen or equal and pull the tray out.
Step 3: power on the Xbox 360 and hit the eject button. When you here the eject "ding" pull the power. Now the drive is in eject mode and the cogs are aligned to take the tray.
Step 4
Gently place the tray back in and slight nudge to engage gears.
Step 5
POwer on xbox 360 and give another nudge to help the tray realign.
Step 6
Open and close the tray a couple times. To assure sucess.