Chosen Solution

I have an old G.E long neck lamp here, and whenever I insert a bulb nothing happens. However, it’s not completely dead because there were signs of electricity within the bulb socket.

Rusty Old Dog use a multimeter and measure for continuity from plug to switch and from switch to socket. Do that for both wires. Check your switch with a multimeter and see if it functions. This could be a bad switch as well as a bad socket.