I have read quite a few problems floating around in the Xbox 360 section where lot of Xbox 360 users encounter Open Tray Error here are some common troubleshooting steps you can try to solve this issue:
First some basic steps to troubleshooting
1) Restart your console.
2) Check for loose cables.
3) Pull out all the cables, and get them back in.
4) Take out the hard-drive, and put it back in. Repeat this 4 times.
Try to use several similar Xbox 360-compatible discs in the console to determine whether the disc that you are using is causing the problem. To test whether the problem is caused by a specific disc, use a disc of the same type, such as a game disc, DVD movie, or music CD. If the problem does not occur when you use other discs, that specific disc might be the cause of the problem.
If you suspect that the Xbox 360 device could be causing the problem you can follow these steps
1. If you have access to another Xbox 360 console, try to play the disc on the other console. Or, if the disc is a CD or a DVD, try to play the disc on another device, such as a CD player, a DVD player, or a computer that is equipped to play CDs or DVDs.
2. If you have an Xbox 360 Hard Drive (HDD) or Memory Unit (MU) attached to the console, turn off the console, and remove the HDD and any attached MU. Then, turn on your console, and try the disc again. If this seems to resolve the problem, turn off your console, reattach the HDD and MU, and then delete any saved games for the game that is causing problems.
If this does not resolve the problem but removing the hard disk does, clear the hard disk drive cache
To clear the cache, follow these steps:
1. Move to the System Settings section of the Xbox 360 dashboard.
2. Select Memory.
Highlight a storage device.Do not press the A button, Press the Y button to view the Device Options screen, Select Clear System Cache, and then select Yes to clear the cache.
I presume you do not have a hacked version of Xbox 360 because this problem is prevalent with Xbox 360 dvd drives which are hacked.
if the above steps do not resolve your issue, please send your Xbox 360 to Repairs, call up MS support and check for the charges of Repairs in case your Xbox is not covered under warranty.
Please do comment on this tip if you find it helpful, Wish you a Happy New Year and Happy Gaming