When I do a search for site:mightycleanhome.com your home page does not come up. That's unusual. It's not blocked by robots.txt and I don't see a noindex tag anywhere.
So, I took text from your home page and enclosed it in quotes and look what I found:
Here's your homepage:
http://www.mightycleanhome.com
and this page is an exact duplicate:
http://mightycleanhome.com/about-mighty-clean-home/
That page does indeed come up on a site:search so it looks like Google has decided that your home page is a duplicate of this inner page. When Google sees duplicates it tries to figure out which one is the original and then only displays that one.
You've also got these pages in the index which are duplicates as well:
Mighty Clean Home House Cleaning Service Roswell Atlanta - Part 12
Mighty Clean Home House Cleaning Service Roswell Atlanta - Part 3
You can fix that by installing the Yoast SEO plugin and marking all "page" pages as noindex.
There are a couple of ways that you can fix the duplication from the about page and the home page. One would be to redirect the about page to the home page with a 301 redirect. Another would be to completely rewrite one of the pages. Once you've done that, then go to Google Search Console (Webmaster Tools) and do a fetch as Googlebot and then click "submit to index". That'll get Google to recrawl the pages and hopefully index the home page.
I'm not sure if these have been mentioned before so forgive me if I'm saying the same thing twice but I'd also make sure you check the manual actions viewer in Google Search Console by going to Search Traffic --> Manual Actions to make sure there is no manual penalty. Also, when you do fetch as Googlebot try a fetch and render and see if Google is able to see the whole page.