Mass Effect 3 Disc Problems

I first bought Mass Effect 3 in early January, do to money constraints, at GameStop. I didn't consider buying the warranty because I bought it brand new and all of my games are in perfect condition and I have never had a problem with the conditions of my games. But I recently have been having problems with my Mass Effect 3 discs for Xbox 360. Originally a couple weeks ago I all of a sudden got a disc reading error, so I decided to reload the game up and it wouldn't load pass the Palaven screen. I decided to see what the problem was and there was a scratched ring around the outer part of the disc. As frustrated as I was I thought I'd wait until I picked up the DLC to re-buy the game and in the meantime play the addicting multiplayer. While playing the multiplayer I was telling a couple of my friends what happened to my disc and two out of the four I talked to about it mentioned that the same thing has happened to theirs. I continued to play the multiplayer the upcoming weeks when all of a sudden my xbox froze. I thought nothing of it and started my xbox back up and unfortunately Mass Effect 3 wasn't loading again. I took a look at the disc, and low and behold another ring on the outside of the disc.

I became very frustrated that this problem didn't only happen once to me, but twice! I absolutely love the game and have played over a hundred hours over just the last three-ish months. I don't know what the problem is but I have heard multiple reports from friends that the same thing has happened to them too. I decided to look up any disc scratching remedies and read that companies such as GameStop and Family Video will buff out the discs for a charge. Hearing this I went to the nearest Family Video and paid $1.99 per disc to get the discs cleaned up, looking at the discs their machines did a decent job. But again when I put them into my system the game will not load past the Palaven screen. I am beyond frustrated over this, seeing as I now have spent $40+ on Mass Effect 3 and now I'm gonna have to spend more money to buy a new game. I sincerely hope you guys have a solution for such a problem with the game.