How can i diagnose a failed Install of Snow Leopard?
This has happened to me in the past. The solution that worked for me was making sure that the disc surface is clean and scratch free, and I mean very clean. Using normal CD wipes is good to get dirt off, but if it is scratched more than slightly, then you may have problems.

Or the disc may be defective from the factory, it does happen and they do exist. 

Try talking to your local Apple Store about a possible replacement, or if worst comes to the worst, you can order one here (Apple still stocks them).

Hope this helps!