iPod touch connects to WiFi but cannot reach internet sites. Any ideas?

My little ten-year-old-or-so iPod Touch cannot, AFAICT, get to any internet site. Neither by browser nor by apps. The problem does not seem to be connecting to WiFi. I select a network, give it the password, wait a few seconds, and then at least it thinks it connects to the network. It gives a checkmark next to the network name and no error messages. But then I cannot get to any internet site. Every site I try gives a message like "Cannot connect to ..." or "Server not available ..." This is not a problem specific to my home WiFi; I have tried this on four different WiFi networks, all giving the same result. I have tried some of the common solutions to the problem of not connecting to a network in the first place (let me repeat, that is not the problem). Other than that, I don't know what to do. Any ideas? One more thing: The last time I tried to connect was a couple of months ago and it worked fine. No idea what could have changed in the meantime.