Ok. It looks like this is a somewhat old thread and the "digging around with a paperclip, toothpick, etc." method works pretty well for everyone. It, however did not work for me. So, with an electron microscope, I peered into the headphone jack on the phone... I noticed at the very top of the 3.5mm hole there is a shiny copper connector at the front side of the hole, that, if you push on it with a toothpick, it moves. Sort of like a tiny switch. Whenever I push the headphone cord toward the little switch, the music cuts out.
So I took a tiny plastic sticker that happened to be laying around and cut a thin strip off of it (about 1/8 inch x 1 inch), then wrapped it around the "top" of the connector on the headphone cord. ABRACADABRA!! It works with no problem! Music doesn't cut out anymore even when I giggle the cord. I assume that little switch (as I so like to call it) must be for a headset with a mic?? Either way, this is my fix and I thought I would share in case anyone still had problems!
I tried to upload pics from my other phone but I'm not sure how on this forum :'(