Test your non-contact voltage tester on a known live circuit to ensure it works. Stick the tester in the smaller slot of your receptacle. It should beep and light up. Flip the corresponding breaker ...

Its easier to fish the new cable if you remove the existing box in the wall. Fiberglass boxes can be busted out with a hammer and a chisel or sturdy screwdriver. Its best to cut the nails on plastic ...