Welcome to TSF,
See
this thread. Different laptop but might be the same problem and same repair. Note that you don't have to have the heat symptom to have the same problem - yours is one of the other symptoms. Often times you can see if it's the problem by looking at the jack and wiggling it or by looking at your leds and wiggling. A hair's width of movement can cause it.
Could also be the cord itself. Some tend to break internally at the DC plug
Bill