First you need to check along that burnt wire for a chafe or rub through that may be causing it to short. Also check for corrosion at the plug, which can cause resistance and heat. Tape up or repair and damage you find to that wire first. Then you need to check for a blown fuse, likely labelled CLOCK or MEM that most likely blew causing a loss of power to the clock. Don't replace the fuse without finding the short or you could do some pretty expensive damage.