If you didnt check the plug for current with a voltmeter, you have no way of knowing that there's no juice coming from the plug. Replace the actual socket with a new one. They're very cheap, like $10-$15 at Autozone.

A voltmeter is one of the handiest tools you could have. Replace the batteries on it, use the selector dial to choose the mode that checks continuity and touch the two leads together, the needle should jump or indicator should light up.