Plex Media Server for Mac with a Pansonic Viera TC-P50S30
First, make sure you have the firewall turned off on the Mac.

Can your TV pick up anything else on the net?

Next, make sure that your router is broadcasting UDP packets. Some routers do not, they swallow UDP.

Now check that Plex Media Server is running right and listening for connections. At the command line:

sudo netstat | grep 'Plex'


That should give you a list of ports that it is using. They will include:

TCP 32400     (for access to the Plex Media Server)
UDP 1900      (for access to the Plex DLNA Server)
TCP/UDP 32469 (for access to the Plex DLNA Server)
UDP 5353      (for Bonjour)


So then you know that it is up and running.

Make sure both your TV and Mac are thinking they are on the same subnet and that the netmask is correct on both.