Diagnosis
The internal heating element has likely failed or there's a break in the circuit from the base to the barrel, a known failure point for older models.
How to Fix It
First, check the wall outlet and try a different one. Unplug, let it cool completely, and inspect the swivel cord connection at the base of the iron for any visible damage, fraying, or looseness.
If That Didn't Work
The issue is internal. These irons are not user-serviceable. Your only path is to contact Hot Tools for warranty service or replace the unit.
Heads Up
Don't attempt to disassemble the iron. The internal components are sealed and you risk electric shock. A persistent cold iron with the light on is a definitive sign of internal failure.