It's been like that for the last two weeks; at least, every time in the last couple of weeks I've turned on the tv it's been doing that.
I am a doofus.
It was the cable running from the cable box to the tv. At least it was Dale who discovered and fixed the problem, rather than a cable company tech. (I hadn't ever called them about it because it was always intermittent. And I didn't want to call about it this time because our house is squalorish and I couldn't stand the idea of someone else being in it.)