A sign that there is a broken speaker in the Boombox is a slight humming or buzzing noise. The sound maybe very subtle, so it is advised to turn the volume higher in order to increase what little noise the speakers make. There is additional information at this troubleshooting page

You may need to wipe the area under and around the switch to make sure nothing is preventing it from moving. After the button is sufficiently cleaned, try moving it into position once again. Try using this troubleshooting page

Logitech UE Boombox can have three devices paired and connected simultaneously. After the first device is connected, to connect another device hold down the Bluetooth botton on the left side of your Boombox until you hear a tone and the LED around the Bluetooth button will indicate pairing is ready. Select UE Boombox on your Bluetooth connection menu and your second device is ready to play audio. For more information on the problem try using this troubleshooting page