Sorry for ressurecting the thread but apparently this can still happen so it is worth it to have a solution out there!
For the past two weeks I had almost exactly the same problem - tiny old TV which worked like a charm with Chromecast 3 and then a bigger "better" Panasonic Viera. Wouldn't budge. And finally, after miles and miles of reading crap like "Check your Wifi" or "Try different HDMI port" i finally stumbled upon an article on How To Geek about the HDCP mechanism and how it mostly makes normal users' lives difficult, instead of preventing piracy. And how to circumvent it in case it's the root cause - and it was, and the fix is tragi-comic - you need a cheap, active HDMI splitter that works with HDCP-enabled devices, yet, essentially circumvents it, because that what's causing a perfectly fine Chromecast to not talk to a perfectly fine TV set. I bought mine online for under 9 bucks. It's a square, metal, black box. No bigger than a box of cigarettes, with one HDMI in and two outs, and an external power brick. Works right out of the box, no configuration needed. As an added bonus, let's your single Chromecast be attached to two different devices at the same time if you ever needed such a thing.
God, that was frustrating!