How does the mobile 3.5mm audio port work, and Can I light a LED from it?
If you must light your led without an external supply you could consider a small audio stepup transformer.Perhaps something out of a dead transistor radio.Otherwise you could build a diode pump that say quadrupled the voltage.Use shottkey diodes for your diode pump because they waste less voltage .Use a red led for your experiment  because they need less volts than the other colors.