I have never heard this issue before. You probably have a lager issue then what can be resolved here and might face future issue in the future. Is this the only game you are having issues with?
Seeing that you mentioned you have purchased a hard drive then I would recommend you install the game to your hard drive and try play after that. This will resolve any issues possably of your disk drive possably getting hung up during gameplay.
follow these instructions to get your game installed on your hard drive:
Install Xbox 360 games on your hard drive from a game disc
Installing an Xbox 360 game on a hard drive requires between 4 and 8 gigabytes (GB) of free disc space.
- Insert the game disc into the disc drive.
Note After you insert the disc, the default option is to automatically start the game. If the game starts, exit the game, and return to the Xbox Dashboard.
- From the Xbox Dashboard, go to My Xbox.
- Select the game you want to install.
- Press Y on your controller.
- Select Install to Hard Drive.
A progress indicator appears while your game is being installed on your hard drive.
- Installing an Xbox 360 game might take several minutes.
- Multidisc game? Install each disc to your hard drive.