There are no errors (I wish there were, it would give something to start with).
If the request form is completed by entering an unregistered user (Name and email), there is no subscription entry made in the database. I am using one of my alternate email addresses and it is a valid functioning email address. I have enable WP_DEBUG, but nothing there indicating an issue.
This is a new install on a GoDaddy managed WordPress 4.7.3 site, ALO EasyMail Newsletter Version 2.9.3 and everest64 Version: 1.1.4 theme.