It seems the hardware was fine, but a brand new ethernet-free lappy fresh-installed with a manufacturer-supported OS according to the manufacturer support phone desk's instructions didn't have a compatible driver. Does anyone even think about driver availability?
Insert the generic dongle, pick a wifi network, lock up for lunch. Come back, eject dongle, and presto! The on-board wifi does what it should've done if the manufacturer thought for five seconds about the driver.