OK, so i dsabled the DHCP server on the LAN interface, turned off the TV turner, turned on the pakcet capture with the interface Set to LAN and the MAC address of the tv turner and then turned on the tv turner. After about 30 seconds this is the only output i got
05:14:49.710584 IP 0.0.0.0.68 > 255.255.255.255.67: UDP, length 300
As you can see, not only the activity was minor but it happened at 05:14 am. The DHCP logs shows nothing after 05:06 am. This tells me that this tv turner is not requesting an IP address (just like the NEST that @KOM mentioned).
I also went to the arp table and, sure enough, there was the tv turner with the ip 10.0.0.10 saying it will expire in 371 seconds.
arptable.jpg
But, the device was not reachable when i tried to ping 10.0.0.10.
arptable2.jpg
Now, at this point i have not enabled the DHCP server yet, so that might have explained why it wasn't reachable.
Anyway, since the IP was supposed to expire in 371 seconds, i just waited 10 minutes to see what was going to happen. I started the package capture again, restarted the DHCP server and the results are as follows:
The package capture got nothing.
The DHCP logs showed that the tv turner requested a new IP and obtained the address 10.0.0.100 which is in the range of the DHCP server.
arptable3.jpg
Now the tv turner is obtaining its IP address from the PFSense's DHCP server as expected. I guess the only thing that i needed to do was to "bounce" the tv turner and disable/enable the DHCP server to fix this situation.
Thanks to all for the pointers on how to fix this.