Test email works but never arrives?

First of all, thank you for this plugin.

I use woocommerce and have not been getting new order notification emails. The email address it is supposed to go is not hosted with the same company as my woocommerce site. I am not sure if that makes a difference or not?

Anyway, I set up everything with no errors. I have sent the test email that appears to go through but then never arrives. I am not sure what else to do?

Here is the information requested for troubleshooting.

OS: Linux gator4044.hostgator.com 3.12.35.1418868451 #1 SMP Wed Dec 17 20:10:32 CST 2014 x86_64
HTTP User Agent: Mozilla/5.0 (Windows NT 6.3; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/43.0.2357.134 Safari/537.36
Platform: PHP Linux 5.4.38 / WordPress 4.2.2 en_US
PHP Dependencies: iconv=Yes, spl_autoload=Yes, openssl=Yes, sockets=Yes, allow_url_fopen=Yes, mcrypt=Yes
WordPress Theme: GoodStore Child
WordPress Plugins: Akismet, Contact Form 7, Envato WordPress Toolkit, WooCommerce shop to Facebook, Flat Rate per State/Country/Region for WooCommerce, Image Widget, JaW Menu, JaW Shortcodes, JaW Widgets, MOJO Marketplace, Postman SMTP, Revolution Slider, Theme Authenticity Checker (TAC), TaxJar – Sales Tax Automation for WooCommerce, Ultimate Social Media and Share Icons, Woocommerce Advanced Free Shipping, WooCommerce Stripe Gateway, WooCommerce Order Status Control, WooCommerce PDF Invoices, WooCommerce Print Invoice/Packing list, Woocommerce Products Per Page, WooCommerce Quantity Increment, WooCommerce Quick View, WooCommerce Shipment Tracking, WooCommerce Smart Coupons, WooCommerce Social Login, WooCommerce Sold Out Products, WooCommerce, WordPress SEO, WP-SpamShield, MailPoet Newsletters, YITH WooCommerce Wishlist, YITH WooCommerce Zoom Magnifier
Postman Version: 1.6.23
Postman Sender Domain (Envelope|Message): ellimod.com|ellimod.com
Postman Prevent Message Sender Override (Email|Name): No|No
Postman Transport URI: smtp:ssl:plain://gator4044.hostgator.com:465
Postman Transport Status (Configured|Ready|Connected): Yes|Yes|Yes
Postman Deliveries (Success|Fail): 0|0
Postman Bind (Success|Fail|Path): Yes|No|/home4/ellimod/public_html/wp-content/plugins/postman-smtp/Postman/PostmanWpMailBinder.php
Postman TCP Timeout (Connection|Read): 10|60
Postman Email Log (Enabled|Limit|Transcript Size): Yes|10|128
Postman Run Mode: production
Postman PHP LogLevel: 40000
Postman Stealth Mode: No
Postman File Locking (Enabled|Temp Dir): Yes|/tmp

https://wordpress.org/plugins/postman-smtp/