Mail won't go online for any of my email accounts

I've woken this morning to a mail software that won't go online. I have several email accounts running on two different servers (.me and a third party server).

I have tried going online, I've tried closing software and re-opening. No luck. I have an internet connection and can access web pages, stream video, etc.

Apple Mac 8GB Memory, 3.06 Ghz Intel Core 2 Processor, OSX 10.9.5

Any ideas?