oddly, the same thing happened to the fan of my car's engine a year ago. wouldn't work until it contacted metal. turns out the fan switch was burned, but i did a temporary repair along the lines of what you could do.
i carefully inserted a paperclip through the wire insulation, and wrapped the copper around the ends of the paperclip and covered it with electrical tape, a few layers of it for assurance. the trick is to cut the paperclip (or pin, depending on how narrow the insulation is) to the right size and make sure the copper ends are still touching eachother when they're wrapped around the pin. it's a delicate procedure, but that's what ghetto technics repair is all about ;)
you might not need a soldering iron, but you can get one at Harbor Freight Tools in O.C.
i would suggest trying other methods first that are sure to get the job done, but this one worked for me and i drove that car for many more miles. hopefully it'll fix your headphones. good luck.
No solder as of yet. I am just so happy that I got it to work.
The headphones themselves look like high-end cans from the late seventies. They sound as good as my Sony Pros and are yet more comfortable.
What I did was take a two inch strip of 18 gauge speaker wire, cut the plastic that houses the copper and then unwrapped the actual wire leaving me with small bits of wire which I carefully wrapped around the original wiring. I did not even have electrical tape to reseal the cable yet but I wrapped that wire so tight it ain't going nowhere.
Solder flux may be required. Solder ribbon/sucker optional. The flux helps make the solder stick to things when it isn't and the sucker or ribbon is to pick up any excess.
Speaking of OLD...my pops just hooked me up with a Toa RXA-212 mixing amp. Don't know how old it is but it was in the church where my dad goes for the past 20 years. 12 channels & 130 watts x2. He said the power is intermitten but can fix it.
christopher we fix headphones all the time at work, if you mail it to me it won't cost you anything except the shipping. i just pretend its my personal gear and the service manager fixes it for free for me. PM me if you're interested.