I have same problem. Tried the needle suggestion. Not so easy! I rarely use headphones and have had this phone for about 1 1/2 years. Everything has been OK until now. Can't hear a person on a call unless I use speaker phone. Can't hear navigation unless I use headphones. What a pain. Really a fatal flaw. Would not recommend a Nokia based on this.
This one issue doesn't mean there is a problem with Nokia, all phones have issues. Having said that, this issue sucks. We have two 928's in our house and both have been great. Unfortunately just like you, one of them experienced this problem. It appears that after many years of use that the headphone contacts gets stuck. I used a thick sowing needle to to unstick it. It took patience and determination, as it took 30 minutes to finally get it unstuck. Unfortunately we can't use the headphones on that one phone fear it stuck again, otherwise it still works fine. We had a good run with 928's. We have since upgraded to the 959XL's on ATT and so far are satisfied.