Casio KX-101
The Casio KX-101 is a 3-piece boombox with AM/FM radio, a cassette player, and a 37-key, 3-channel keyboard. It might qualify as having the highest number of switches ever put onto a boombox! It takes eight D-cell batteries, and was sold in 1984.
For much more information, including internal photos, see this page: http://weltenschule.de/TableHooters/Casio_KX-101.html