Mr Draper,
Let me guess, the telly has a self-assigned address from the 169.254.0.0/16 range because its unable to sort itself out over DHCP ?
Does the telly have a USB port, is a software update and/or management tool available from the manufacturer website ? Have you researched the possibility of a "hidden/engineer" menu ?
Have you tried updating the software on the router ? Reserving an IP for that TV based on its MAC address ?
Sometimes you do come across devices that, for whatever reason can't manage to talk to a given DHCP server. Quickest fix is manual settings.