I have these problems once in a while. Here's what I do.
To get the disc drive open wedge your fingernail into the left side of the disc drive and apply a little pressure towards the right, then while your putting pressure on the disc drive either press the open button or the x button to open it and remove your hands 1 second after you attemp to open it. And that should get your game out, leave the disc drive open for the time being.
Now to fix the 360's reading problems first blow into the disc drive that is still opened. After that close the disc drive, unplug everything from off of your 360, and take your harddrive off. Now blow on every opening on your 360, air vents, memory card openings, USB openings, ect. Make sure you blow every little piece of dust out. Then let it sit for a couple of minutes, plug everything back in and it should hopefully work.
Also I find its easier to open up the disc drive if there is a game in the 360. You may also have to use the procedure up above every time to open your 360's disc drive.
