Question: I am running a .NET web application in its own application pool on IIS7. The parent website is set to run in its own application pool. Today we noticed a huge number of connections going to IIS. I tried to browse a plain ol' .html page in the directory of the web application and it hangs. I then try to browse another plain .html file in the root of the parent website, and it too hangs.

In performance monitor, i see there are some 8k connections to the default website and climbing. I cant seem to understand if my application was the problem, or IIS itself.

If it was my application, wouldnt the html page in the root of the parent website still be able to be served?

edit: Also, if i shut down the app pool to my application, the html page on the root of the parent website is still not able to be displayed.

Answer: 
Mike, the short answer to the question in the title is "No". Every application that has its own application pool, doesn't inherit any other application pool.

But it seems to me that the problem is somewhere else. I'm not very familiar with Windows' TCP stack and connections limitation, but it is possible that IIS itself (the main process that routes requests to the various applications and application pools) causes the problems. This would explain why shutting down your application didn't help making IIS more responsive.

Are 8K users the norm for this site? It this just a one time peak?

Also, try to provide some more information regarding the configuration: amount of RAM, the nature of the applications (static HTMLs? ASP.NET?), etc.
I don't believe so. Sounds more like your server is running out of resources due to the number of connections. Have you tried running perf monitor to check? You could try putting a limit on the connections to your app also.