I used to get this message as well, the 360 read everything no problem then one day started coming up with the Open Tray message with a disc in that previously worked fine, and would do it with all discs including dvds.
The drive would try to pick the disc up and spin it, but would fail each time with a kind of whirring clicking noise.
This is going to sound ridiculous but I used a piece of card to adjust something in the disc drive without taking the thing apart- at work but will post link later.
It worked for me, havent had any issues since, of course if its still in warranty etc then you may be slightly reluctant to try it, although its veeery simple to do, must be nearly a year since i had to do it and its been fine since.