I tried that.
I’m not sure what you’re indicating; that you’ve actually confirmed that your site is configured to serve index.php files by default, or that you’ve contacted your hosts support group for assistance..
This displays: nathanrhowe.com/readme.html
as does this nathanrhowe.com/wp-login.php
As you can see, pages that are “not” named index.*. seem to display properly – both .html and .php.
The home page is normally displayed by rendering an index.php page. Which so far, still seems to be something your site is still having a problem with.
You can try replacing the default index.php file in the root of your site (and maybe also the one in your active theme) with a fresh copy from the WordPress package, and see if that makes a difference. It’s possible that it might be corrupted/damaged in some way.
If that doesn’t change anything, contact support at HostGator. Maybe they can point out something simple that’s causing the index.php page not to display.
[edit] This seems to work: nathanrhowe.com/about-the-authors/