Have you checked your account settings with regard to the outgoing mail (SMTP) server?
If it's working on one machine, and not the other, the first thing I'd suspect is that either the server name, port number, security type, or login requirements for the SMTP server somehow got messed up.
Compare what they are on the functioning machine and on the "doesn't send" machine and tweak as indicated.
If this doesn't turn out to be the situation it would be helpful to know the respective e-mail clients you're using at a minimum.
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1803, Build 17134
In a modern society where everyone thinks their opinion deserves to be heard nothing annoys me more than individuals who mistake their personal preferences for fact.
~ Commenter TheCruyffGurn on the The Guardian website, 8/13/2014