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.