Not sure where the location of your socket is but if you can access the rear of it and test for power @ the connection to make sure there is power going into it then you'll know what's the next route you need to go.
1. If there is power @ the wire, just go to your local automotive store and pick up a new socket and replace it. 3 bucks and 15 minutes and you're back in business.
2. If there are no power coming from the connection then there is only one simpliest option I can think of. Find a constant 12V source anywhere in your vehicle not sure what color usually yello or red if I can recall but don't count me on it. Use your Volt meter to test the wire with the ignition off and key out. WHen you find 12v tap into that wire with your desire inline fuse and tap back into your cigarette lighter. Assuming that there were no previous problem with your current socket you should be up and running other wise go back to option 1.
BTW I would cut away the stock wire away from your new connection just in case there's an opening along the stock wirings.