This from here "Debris in disc drive
If your disc drive tray is stuck and will not open or close, then you have to manually eject the disc. Follow these instructions to remove the faceplate and manually eject the drive. Remove any obstructions, and plug the console back in. If the eject button still doesn't work, your disc drive may need to be replaced."
In general, for any optical drive, you want to check the following:
Stuck disc or other object in drive
Remove the disc
If there is a disc in the tray remove it.
Disc drive button broke
Bad drive gears
there is also the possibility that your drive does not read the disk (try other ones) and therefore opens the tray. That would also be connected to the flashing green light, since it indicated that your drive is trying to read a disk. You might try to clean the laser of your drive, or think about replacing your drive. Just remember "The Xbox 360 is designed so that the DVD drive works only with the particular game console it is installed in. Replacing a defective DVD drive with a replacement DVD drive does not work, since the replacement has a different DVD drive key, which the game console won't accept. ...Hope this helps, good luck.