Often, it's a simple problem:
The cable is broken.
So, why don't solder an other cable on the headphone?
What we need:
-new headphone cable (3,5mm)
Step 1: Open Your Old Headphones
Please, don't cut yourself!
Step 2: Unsolder the Old Cable
Then unsolder the old cables and remove them.
Step 3: Solder the New Cable On
Close the headphone and glue it together.
Step 4: Test Your Repaired Headphone.
If it don't works, then unsolder the new cable and buy a new headphone. Or test another cable.