You either need to empty your registry and un-used files with a program such as Regseeker or Advanced System Optimizer
http://download.com.com/3000-2086-10147659.html- Advanced System Optimize
http://www.snapfiles.com/get/regseeker.html- Reg seeker.
If you remove older registry files and un-used files the computer will most likely give you the opportunity to reinstall the game because it will not have any data stored concerning your install. No important data, that is.
Be careful when using these programs, follow the instructions and if you're not certain ask about them on this forum.
If you have done this, and the disk still refuses to uninstall, return it to the store and ask for a new one. If there's still a warranty on your disk.
May I know the name of the game?