Messages app stopped sending iMessages
I have had a similar problem in the past when upgrading OS. The easiest way to fix it I found was to disable iMessage on the faulty machine and then re-enable it. 

To do this:

Messages > Preferences > Accounts > Click your iMessage account > uncheck "enable this account" > sign out > restart Messages > sign back in. 

You may need to follow the steps above to recheck the "enable this account" box.