receptacle not working in kitchen
Since you only have three conductors in your junction box, it means you are at the end of that circuit. The burning of the insulation is a concern and probably indicates that you have had an overheating problem and that has probably caused your failure. You need to trace back to the preceding box and check it for loose connections or some other failure. Just because the preceding receptacle is working does not mean that there is not a problem in that box. (forgive the double negative). I have attached a rough drawing to let you know what you are looking at.
 

If you can't find the problem in that box the you have damaged your wiring and you will need to ring out the circuit to find the problem.

Good luck