If you are unable to clean/scrape out the melted plastic from the 12 volt power socket you will need to replace the plate. That plate is also the 12 volt power supply booster amp for your OTA antenna.
You can find it at most RV supply houses or of course Amazon
Be sure to note the coax and power connections when you remove the existing plate. You should have the power feed and 3 coax cables to the rear of the plate.
As far as the plug on the cord, you can replace it with a standard replacement plug that you can obtain at any auto parts store. There is nothing special about the Jensen factory plug.