You should do this:
Turn off everything, and push the A button on the Wiimote, if the 4 leds blue lights flash, then it has 100% battery, if only 3 leds = 75%, 2 leds = 50 % etc.
If it is not the batteries, then unplug everything, then after at least 5 minutes, plug everything up again, if the wiimote is still with problems, hold down the sync button on the console for 15 seconds, then turn it off again, turn it on, hold down the sync button in the console and wiimote 15 seconds more and then start playing.