I've held down the power button and it isn't turning on, no matter how long I hold the button down for.

I had the same problem with my LeapPad3. Always turn off your device and turn it back on again, as this can solve a few issues your device is having. If this doesn't work, you will have to remove the back cover of the device and tighten the cable connecting the speaker to the motherboard. If that doesn't fix the problem, then you may be forced to replacing the speaker itself. There is a guide 'here' that can help you through the process step-by-step. Good luck!