Image compression? Images are already compressed. You are not attempting to compress them again, are you? I didn't see any evidence of that, but I have to ask.
Your main page has 50 requests. That is a lot, but not the root of the problem. tools.pingdom.com indicates the wait time to receive the HTML of your index page is over 20 seconds. :eek: That's some of the worst performance I have ever seen outside of a shared host I used years ago. On the first load, all of your files took a long time to be transmitted, including the images, CSS, and JS. On secondary loads, the HTML still took over 20 seconds to be received but the linked in files took less time. That seems to indicate the bottleneck is in the page generation somewhere.
Are you running any type of PHP accelerator? It looks like you are using PHP 5.3 which was released in 2009 and for which support will end in July 2014. You should consider upgrading to PHP 5.5 if your code will allow it. Significant improvements in performance have been made since 5.3. Plus, 5.5 has an available opcode cache that can help improve performance. But I don't think that will help in your situation.
For now you must simplify. Turn off output compression for starters and any other special, non-essential configuration features. If that doesn't help, you will have to start profiling your code and database queries to find where the trouble is. You have a powerful VPS. No way should it take this long to load a page.
Right after I posted this I saw the original poster's reply and tested his site again. The main HTML load time has declined from 20 seconds down to 0.723 seconds. I think the OP fixed it.