If you could not turn on your Magic TrackPad, if you're press the power button on the peripheral, but it doesn't light: one of the reasons is a faulty contacts. Open the battery module. Remove the batteries. Take a long screwdriver and put a bit of cotton on its end. Wet the cotton by the medicine alcohol. The carefully move the end of the screwdriver with the cotton into the battery module and carefully clean the remote side of the module (you can see the metallic contact there). Then carefully clean the screwing cover of the module. Wait about 10-15 minutes until the medicine alcohol evaporates. Then put the batteries back, screw the cover and try tu turn on your Magic TrackPad by its power button.
Warning! Don't use a huge peace of cotton and much medicine alcohol, you must clean by it, not wash in ;) Don't hurry up after the cleaning: wait until the medicine alcohol evaporates, only then you can insert batteries. Don't use drinks like whiskey, they have components that will not evaporate and the device will be broken. Use only clean medicine alcohol.
P.S. If you can't repair the TrackPad, maybe its hardware is damaged.