So in a nutshell this is how I see the problem:
Somthing on your website is trying to use the following file:
but it cant be found so pingdom.com or the site hangs.
And there are other mystery files that cannot be found.
I have w3tc installed on two websites and I have no files of the type default.include.xxxxx. nor do I have any directories under the directory "min". But you may have enabled different options in your w3tc cache settings thus accounting for the differences. Without system access this would be difficult to find, if at all.
1. You might try to test your site using blitz.io and see if you get the same results. Maybe the problem is with pingdom.com and not you. Your site does not seem particularly slow to me. But that is a subjective observation.
2. You might try removing the w3tc cache plugin and resinstalling it.
Other then that I have no othe ideas. Good luck.