You’ve turned on SSH, and even enabled the firewall profile for SSH. But for some reason you still can’t SSH into the ESXi server and get a “Connection Refused” message back when hitting port 22. You’ve also checked your corporate firewall and that’s it’s not blocking comms.
Have a look in Tasks and Events to see if the server’s ramdisk for root is full. There’s a good chance that it is. This is a problem i’ve encountered with vSphere 5.1 recently and is preventing SSH from starting properly.
The cause of the ramdisk filling up is ESXi not truncating /var/log/wtmp properly. That’s another issue, but to fix the immediate problem, vMotion all the VMs off the ESXi server first. You may get errors like “Cannot migrate <vmname>”. It’s all because of the full ramdisk. You can often give it a kick by re-running DRS for the cluster and that gets it going again.
Once all VMs are off the server, reboot it and your problems should go away.