When on the host server itself, using it's display, keyboard, etc., (the four colored screen) go into the Management Network and make sure the correct IP is assigned to it, with the DNS server address (IP) and the gateway for your network too. Make sure all the DNS settings are correct (in the additional listings) and then make sure at least one network adapter is listed for the management network.
What do you get for results when you use "Test Management Network"? Did you set any VLANs within the management network? If you did, try removing that setting (at least for now). Also make sure that the host is in your DNS forward lookup tables correctly. I've had to manually add ESX/ESXi host servers there before, since the DNS servers took too long to discover the hosts, and I didn't have several hours to wait to connect to them.
Also try restarting the management network right from the host.
With the correct settings on the host, and the entry in DNS, you should be able to connect to the host either through it's IP of FQDN.
I would also make sure the cables were run correctly from the back of the host server to your LAN... Confirm that you have the correct port to the correct switch/segment of the network and that it can communicate back to the rest of the LAN...
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