Help - Problems installing Snow Leopard on Macbook

I'm having trouble installing a brand-new copy of Snow Leopard onto my Macbook. It loads just fine, and I'm able to start the installation. Halfway through the process, the computer restarts itself and cancels the installation.

Occassionally I get a warning sign from the installation program that says it can't read the disk and that it needs to be cleaned. The disc is brand new and isn't scratched so i'm not sure why it's giving me that warning. Anything I can do to fix this or do I need to get the disc replaced?

 

I will try other discs and see if they work. What's weird is that the progress bar gets very close to the end.. and when it's at 80% complete, it shuts down.

It's a brand new hard-drive that I replaced myself. I was able to do a full-restore from my Time Machine backup with no problems before this.

It's a brand-new disc that I purchased at Best Buy.