You can add your web site to an empty solution (giving you a .sln file), then call msbuild.exe using the exec task against the solution file, or use NAntContrib's msbuild task.
For deploying, since it's a website, you have two options: either copy the files directly to the target location, or first precompile with aspnet_compiler.exe, then copy. See this MSDN article on more info on precompiling.
Your build file will contain roughly the following tasks:
- MsBuild
- (Optional) aspnet_compile
- Copy to destination location
Plug that into cruise control and you should be good to go (though I recommend separate build configurations for 1 and 2 vs 3).