I have a ceiling light in the laundry room that flickers but won't stay on. I changed the switch and now it does nothing.I put the old switch back in and tested the voltage. Both neutral and hot register 120 volts. If I wiggle the switch the light will come on .Is there a broken wire somewhere? What should I check for?

If the wires were pigtailed to the switch, I would suspect a loose connection there. If the black is straight wired through the switch, it could be back it another box supplying power. Doesn't sound like a bad switch, the new one would have corrected that.