[fore-warning: I am not a member of Xbox Support, just another user like you.] Decided to post here because it seems like there is some air that needs clearing regarding this issue.
So lately I have been hearing that many users have been affected by the new update being pushed out to your xbox between May 19th and May 31st, and now are unable to play. You may be experiencing that your console can no longer read disks, or can no longer connect to xbox live.
There have been press releases regarding your issue if your Xbox can no longer read disks. You may have recieved an email from Xbox Support regarding this. If you haven't, you may not have your console registered or they have contact information that is not up to date.
You may view the following links for more information.
If you did not recieve an email, I would suggest calling Xbox Phone Support to let them know about the issue you are having. They will most likely ask for your serial number. You may find this on the back of the console by the barcodes, or you can go to System Settings -> Console Settings -> System info to find it as well.
I have also been seeing some issues occuring that some consoles can no longer connect to live after the update. If you are having this issue, calling Xbox Support is going to be your best option.
Any questions you may have, should be directed to Xbox Phone Support. 1800-4MY-XBOX (1-800-469-9269)
edit: adding paragraphs