First, make sure that disc is clean and free of anything, such as scratches or cracks, that would cause it to not play. If the Xbox 360 still won't read a game and won't close the tray, check the power button when the tray sticks to see if it is off or on, and/or that the system is plugged in.
Take the disc out of the tray and inspect it closer for any scratches or debris which may hinder it from playing correctly. Do not use solvents on the disc to clean it, as this will only cause more problems.
If the tray is stuck and there is not a problem with the disc, try unplugging the console for thirty seconds and then plug it back in. Doing this will allow the console to reset itself and possibly fix the problem at hand. If necessary, carefully adjust the tray to ensure that it is not sticking, or off its track. If all of this fails, then contact the Microsoft Support center for the Xbox 360 troubleshooting assistance.