Auggius, just wondering, what was your solution for the short stud? The burnt plug is a familiar sight. Did you splice in a new(er) plug or replace the whole harness?
Hmm ... you have to have a cigarette-lighter receptacle in order to use it? Have you used it and does it work more than one time (sorry, can't help it ... after all it's Walmart and it's only $9.99) ;-)