I take it that you get a red X with the timeout?
“No suitable AP” actually means there is no access point, meaning: no available WiFi Network. If you report that there are up to eight, it should at least see one? o_O
I’m going to try that at somewhere where I can easily manipulate the WiFi. Maybe, it only tests connectivity on open WiFi, not on secured ones. Should have seen your open WiFi, then.
Just for the fun of it, you could get Fing from GooglePlay, and try out what it gives you if you choose Discover Wi-Fi. If it’s unable to connect at all, you will get a stupid error message sending you back to the WiFi settings - but if you are able to connect, you should be able to explore the network a bit. (Not that this would help you with it’s output, really - but it would show your modem works.)