I had the same problem. My Big Jambox buttons came off & rubbers went sticky.
I removed the stickiness by rubbing Isopropyl Rubbing Alcohol with a microfiber cloth. Now the surface is smooth.
Regarding the bluetooth connection, press the J button (1st one on the left) 7-10 times rapidly.
On the last press, its very important to hold it down until the power button starts blinking red and orange!
In the pairing mode, you should be able to connect to your Speaker. This worked for me !
Hope it helps!