Mail delivery system failure from WordPress website

Hi, when sending a message via contact form 7 email is not send. It displays message "Failed to send your message. Please try later or contact the administrator by another method." with red border box, which indicates that the problem is in web hosting mailing service. My contact form is correctly set-up, since I have working contact form in another website with same settings + in Flamingo plugin the failed messages are registered to WordPress dashboard, so the error must be in mailing service and I believe is something that can be fixed is in cPanel. I'm pretty newbie what comes to cPanel settings and I don't have no clue how to even check where the problem is in cPanel. Email that is used works fine otherwise. Would anybody know what to check in mailing delivery system and maybe make me a step-by-step list what to look for?