Do you have a pull-out sprayer? The kind with the metal hose? I’ve had junk get caught where the hose screws into the sprayer handle. Try unscrewing that.
I do have a pull-out sprayer. I know it’s not clogged at the handle, because the sprayer is working. I’m tempted to unscrew it at the faucet, but think I should wait till this weekend when I can pick up some plumber’s tape.
Otherwise, with all this weirdness going on, I’m afraid I’d end up with both a leak AND no water coming out the faucet!! 
Thanks so much for your help, Beowulff, and everyone else, too. It has helped me so much reading everyone’s ideas.
If the sprayer works at all, water is getting to the controls for the faucet. The sprayer diverter valve is part of the mixing valve where the hot and cold water come together to come out the faucet. This suggests strongly to me that the obstruction is in that mixing/diverter valve assembly.
If you were planning on replacing the faucet anyway, go right ahead. Otherwise, just get a rebuild kit and take it all apart and clean it up and replace what needs replacing (washers, o-rings, the valve itself, etc.)
I think that’s the thing to do, KneadToKnow.
Here is a simple test. Turn off the shut offs at the sink. Disconnect the faucet. Turn each one on. If you get a good flow out of both, then it is the faucet. If you do not get a flow then keep looking.
Also how old is the house?
Copper, or iron pipes?
What kind of water, well, city, hard or soft.