Is My Onkyo Receiver's Tuner Dead or Just Playing Posum?

No sound or a bad signal? Does it have a setting to mute weak signals? In that case none of the stations in your new location may pass the threshold. Anyway, I would not worry too much. These days internet radio is at least as good as FM, and a Chromecast Audio used with the TuneIn app will give you thousands of stations in often pretty good quality. Not as good as CD Red Book, depending on a station's bitrate, but on balance, and with different strengths and weaknesses, usually better than FM, which really is a pretty outdated compromise technology. We still have a good FM tuner in the main system, but to be honest it sits unused now that we use a Chromecast to stream internet radio (and from all over the world).

So it does have an automute if the signal is not strong enough. Next time you visit a friend or family member in a different location with known good FM reception, take it with you and see what you get there.
Or just move over to internet radio. Internet radio is not perfect, but neither is FM. The deficiencies are different and therefore hard to directly compare, but I think on balance for most internet stations with somewhat higher bitrates internet radio is now superior. And it is only getting better: with more bandwidth by the year, bitrates continue to go up. A Chromecast Audio is only $35, and the inbuilt DAC is more than good enough for internet radio.