A custom made template uses front-page.php for a static homepage, but I can't disable it.

I am having an issue with a website (http://www.levelcloud.net). The template for this site is a custom made template from a 3rd party firm who created it using the Foundation framework.

They added a static frontpage using the front-page.php file. However I need to change this to a static front page the more standard way. Setting a static frontpage to a normal page from Settings -> Reading.

According to the documentation at http://codex.wordpress.org/Creating_a_Static_Front_Page All I should have to do is get rid of (or rename) front-page.php in the theme folder.

When I do this, the static frontpage does not change to the one I have set under Reading options. (Yet the PAGE TITLE changes oddly).

If I get rid of home.php as well from the theme folder, THEN it displays as I want. However.. the blog / posts archive messes up!

I have no idea how to fix this. I want to be able to control the static frontpage in what I think is the NORMAL way. But obviously want the blog to still function.

I've included both the front-page.php and home.php files to make it easier to get some help. If someone knows what is going on, or how I can fix this, that would be a miracle for me!