Used ceiling fan not working
You are testing hot (light socket center) to ground (housing screw) and getting 120 volts. How about between light socket center and light socket screw threads? This will test hot to neutral which is where you need the voltage. Assuming this is not near 120 volts, it sounds like your neutral (white) wire is not connected. You should probably take down the fan and test voltage between black and white wires or, better yet, reconnect the old light to test. Assuming this works, reconnect the fan, making sure the get good connections with the wirenuts.