Some headphone cables have enamel on wires - Meaning, even though the wires looks bare or seem exposed, it is in fact insulated. You will have to scrape off some enamel to expose the copper, and then proceed to soldering it to the new 3.5mm jack.
You can use a hobby blade to scrape it off - google "scraping enamel of wire"
If that fails, then :
Do you have a multimeter that has continuity test feature?
The cable may be broken somewhere along the line.
If you can, post a pic of what you are working on