Mac Mail accounts showing "offline"

Hi:

I am using MacMail (6.6 1510) on 10.8.5. I have two gmail acounts, a yahoo, and two non-web based emails (one is POP, one is IMAP). For several days now, all of the accounts, except the POP (it works fine) are not allowing me to send email. It says the SMTP server is offline. I have trolled these boards for hours looking for solutions.

I have:

• Deleted the gmails and yahoo accounts and re-added. That worked for a couple hours.
• Shut off my VPN
• Tried every port number suggested in the boards on this topic
• Disabled each account and tried the above
• Disabled Icloud

My mail works fine with my phone and my Ipad, with the same settings.

I am not a tech person. I have no tech support and no Genius bar nearby. I have tried everything. I just need my mail to work. My business depends on it. Can anyone help? I have tried switching to Airmail, but I can't live without Mac Mail's rules (and I uninstalled Airmail, in case that's a cause) .

Thanks,

Christy