Recently had my disc drive finally go bad on my launch Xbox 360 (only one RRoD, too). It refuses to read even brand new discs. I just bought Rocksmith 2014 and realized this. My console does however read well enough to recognize games that have been installed on my HDD. I took my Rocksmith and my hard drive to my friend's house where I used his Xbox 360 to install the game to MY HDD.
I came home to try it out and it still gives me a "Disc is Unreadable" error after a few seconds. I bought the game and have all the files for it on my HDD but it just won't function and it is quite frustrating. Buying an auxiliary disc drive is out of the question as this is very likely the LAST game I'll buy for my 360 before I buy a PS4. Any workarounds would be much appreciated.