Turn the sign on by flipping the power switch of the outlet that the transformer is plugged into. Look at the neon sign that is plugged into the transformer. Look for flickering of the light (other than the initial flickering during the warm-up phase of the neon gas). If the light is flickering, then the current supplied by the transformer could be erratic or the neon sign itself could be worn out. If the light does not come on at all, then multiple things could be wrong.

Unplug the transformer from the wall outlet and plug it into another outlet, preferably one that you know provides steady and clean current. Turn the neon sign back on and watch the neon sign. If the sign comes on and does not flicker now, then the problem was the electrical outlet. Have an electrician inspect your wall outlet, as it is in need of repairs. If the sign still does not come on or flickers, then advance to the next step.

Unplug the neon tubing from the transformer (while the transformer is unplugged from the wall). Some neon tubes will just plug into the transformer like a regular electrical cord, while others may require you to unscrew the electrical posts. Use a screwdriver to remove the screw that clamps the electrical connector to the post and then remove by hand (grasping only the insulated wire part).

Plug in a different neon tube to check for power and flickering. If this tube works, then the problem is not with the transformer: Your old tube is worn out and needs a refill of neon gas. If the second tube did not light, then the transformer is broken and needs to be replaced or repaired.