Once you have signed up for Network Solutions email., you will need to check one setting in your Email Account. Log into your email account and look under settings and make sure that the port is set to 25. 

To do that Log into your Network solutions webmail and click your account in the upper right (1), select "Settings" (2), Click "Accounts" in the left column (3), and then select "Edit" on the email account that showed up (4). 

On the window that pops up, scroll down to the section titled Outgoing server (SMTP)  and make sure that is set to server port 25. 

Next, go to your website /aesys panel and log in then click on Configuration > Set up Email. Make sure you're using the mail.yourdomain.com (with your actual domain in place of "yourdomain"). In the example below, our made up email (sales@yourdomain.com) would be set up like this... 

To make sure everything is set up correctly, hit "Test All" and you should see 4 green "success" bars at the top of the page.