Xbox game had perfect circle scratch

Hold the disk to light and look for pinholes through the silver layer.

The disk tray often gets stuck with the older models of the Xbox 360. After opening the tray, lightly spray some WD-40 onto the areas where the tray moves along.
As for not reading games, it's important that you find whether the issue is the game or the Xbox. Try playing the game on another Xbox console. If it works, your DVD drive is most likely faulty.

There isn't really a way to clean it, but you could try either the toothpaste or brasso trick(google it). your best bet would be to buy a disk doctor or take it to gamestop and ask them to resurface it.

Your DVD tray may be misaligned. Call 1-800-4my-xbox to see if your box is under warranty. Something else to consider is if you had the game in the console and moved it with the game inserted. This results in a misaligned disc and when it spins up for loading it scratches perfect circles into the disc.
Any further questions feel free to ask.

http://cgi.ebay.co.uk/CD-DVD-PS2-XBOX-DISC-CLEANER-SCRATCH-REPAIR-KIT-P65_W0QQitemZ260455729179QQcmdZViewItemQQptZLH_DefaultDomain_3?hash=item3ca45f081b#ht_2688wt_939
This is the type of thing you should use, they really do work and you can get them world wide form all ebay sites and shops.
You can also try a home method, this is to use a cloth and toothpaste, toothpaste will act like fine sandpaper and small circle rubbing over the area will buff the scratch out.

This happened to me a few times. if you bump onto the xbox with a game in it, it might make a circle scratch on it. Check for that, and if it isn't there, then mabe try cleaning the disk. I pour some water on the disk and then gently wipe it in a circle with a tissue.

It sounds like the console's reader scratched your disc. This can occur when moving the console while it is on, the disc can slip off and get heavily scratched.

I would try grabbing a blank (unimportant) cd or disc and place it in the disc tray, then turning on the console to see if the console is scratching the disc.

Also, be sure to have the console FLAT on the ground, NOT vertical. This can greatly decrease any chance of the console scratching your discs.

I personally have had my XBOX wreck 3 different game's now due to just tapping or nudging the console. I took my wrecked games to a local used game shop like GameStop where they will take the disc from you and allow a discounted price (usually around $10) for a replacement used game.

There is not much you can do about the wrecked disc. You can attempt to have the disc resurfaced (local video rental shops can do this). Microsoft does have a disc replacement program however it takes weeks to have the game returned, and they only allow certain games to be replaced. More information on that can be found here:
http://support.xbox.com/support/en/us/xbox360/gamesandmedia/games/discreplacement/DiscReplacementPlan.aspx

Hope this helps!

Lazer burn!!!happens to a load of my discs too usually doesnt kill em though

goto www.llama.com they have a lot of helpful information on the 360. they also have a link to a site where you can buy a guide on repairing the 360 yourself for $25.00 You could even use this to start repairing 360's in your area and make some cash!

http://www.llamma.com/xbox360/news/Xbox-360-Game-Disc-Scratched.htm