I'm thinking this might be an issue with your hosting settings. Can I get access to your network solutions account? There might be firewall settings preventing access to your smtp server.
I found this, which implies it may be a network solutions setting that needs to be reconfigured: https://stackoverflow.com/questions/21353213/php-contact-form-with-network-solutions
I'd start a support ticket with network solutions. I think the issue is with your hosting server and not the smtp service.