In spite of my setting up everything according to all the help sites I can find, my Google Cast APP cant'find my TV. It tells me "No Cast devices found." I can verify that I am connected to the correct LAN and that other LANs in the area show up but no Chromecast. My laptop, tablet and smartphone all are able to connect and cast without a problem.
I hope this is just another case of something simple that I missed.
How are you actually connected to the router that the Chromecast is connected to? WiFi or LAN? How does this compare with your other devices?
The root issue will most likely be multicast/UPnP support on which ever adapter you're using, and that's what you should investigate. Also have you tried to temporarily disable any firewall settings on the NUC to verify?