I have replaced the bulb with several new bulbs but it is still not working? Why?

I would look for a GFI Receptacle that may have tripped. Check for power at the switch.

Also check for the eyelet contact at the bottom of the socket. It may be hot, but has ben bent down too far that the lamp cannot touch it.
It may be hot, so be sure the switch is off. Use a small tool to bend up a bit so the contact at the bottom of the lamp comes in contact.