I faced a same problem
What i did was
If your device is on and the button isnt responding
I reseted (turning off) my jbl flip 3 using the + button by pressing it for sometime until the device turned off (red light appeared)
Wait for a little while, about 10 minutes and try to turn on again using the power button.
If it doesnt work try to plug in on a charger and press + continously until the device turned on by itself(there will be red light) and wait again for 10 minutes.
As i know different device has different period of resseting, so if your jbl is little bit old so you need to wait for little longer.
I hope it'll work . Cause it worked on mine.