Zimbra Mail Server, following all requirements, cannot connect to the internet

This sounds like a firewall problem. I suggest you start looking there.

If you mean that the Zimbra mail server cannot connect using internet ports for mail, you need to open a support ticket and request that Linode unblock those ports for your VPS.

— sw

It isn't a firewall problem, as disabling the firewall and trying to ping an internet service again proves.
Plus mail ports have been unblocked on all Linodes.

It isn't a firewall problem, as disabling the firewall and trying to ping an internet service again proves.

I'm missing something here… Disabling the firewall would, of course, allow your Linode to ping and be pinged.

Can you describe your problem in a little more specific detail?

-- sw