"Your accessories may be refusing to work becuase they sense the difference in voltage. Or you just need to push harder or pull the little metal prongs out further"
A difference in voltage. Hmmm. In all my years of electronics theory and car mechanics, I have never run into a different voltage in cars. 12-14 vdc is typical. You might mean a difference in current. Your cigar lighter is rated at 10 amps, Usually. You might see if the accessories you are using have fuses inside the cigar plug. I think those might be blown first. They usually have "fast" blow fuses unlike the regular fuse in your panel under the dash.
I run a gps unit, laptop for gps, and maplight all on the front lighter plug.
Rich