Verify that the machine is indeed off and will not activate. Sometimes the lights on the console turn off even when the machine is active. Press the power button and listen for a beep.
Ensure your elliptical is receiving power by inspecting your home's circuit breaker. If the particular breaker that supplies power to your elliptical is flipped, then your elliptical is not receiving power and cannot activate.
Unplug your Horizon elliptical. Inspect the power cord to make sure that it is indeed the one that came with your elliptical. Ensure there are no kinks or breaks in the cord as these can interrupt power flow. If the cord is damaged, you will need to replace it.
Inspect the console on your elliptical. Find the battery slot and open it. Replace the batteries to see if this solves the problem. Review all the connections on your console to make sure that they are properly inserted. Reinsert any loosely connected cords.
Tighten the bolts found throughout your elliptical. These bolts hold the various pieces of your elliptical together. For your own safety, the machine will not activate if these are too loose.
Activate your elliptical to verify renewed operation.