Hi,
What is the model number of the iron?
Do you have a DMM (digital multimeter) and know how to use it?
It seems as though there may be a problem with the power supply to the iron. It could be the power cable plug or cord (fractured wire perhaps), or something in the iron itself (switch, control board etc).
The iron would have to be tested to know what and where the problem is.
If a part is faulty (asides from the power cable and plug) getting replacement parts may be difficult as usually these types of appliances are considered disposable when they fail and no parts are available.