Ok, so the mystery seems to be solved. According to the Sr Sys Admin that looked over my account, the problem is the combination of K2 and mod_news_pro_gk4, with News Pro being the primary problem. As you can see from his message (below), the load time of the page was reduced to less than 2 seconds by simply turning this module off.
Now, I like this module so I'm not going to rag on it. Of course, that also means I would like to continue using it, even though I find a 40 second page load to really be unattractive (to say the least). So now I'm wondering if there is something I can do to speed up the performance of this module, or if it really is a situation where I have to choose between the module and fast page loads.
I have thoroughly investigated your Joomla and I have found the reason for the 30+ Second page load times;
There are two modules/plugins that are causing this in conjunction. This is System-K2 and mod_news_pro_gk4 in conjunction.
If I disable mod_news_pro_gk4 by itself it bring down the load time significantly as well, so that module is the main issue.
However, by enabling joomla cache and disabling mod_news_pro_gk4, I was able to get your site load time to 1.5 seconds which is pretty good with the large amount of content and joomla modules that initially load.
I also verified that all of your databases are proper with no errors. They are in excellent health.
However, that module seems to be the main culprit for the awful load times. I would see if you can some how replace the module with an alternate one that functions similarly or you could contact the developers of that module and see if they can't help you with it.