The light on the inverter is to notify you that it is connected properly and has source power. The light does not tell you if you have 120v.
Test the inverter by using a desk lamp with a incandescent light bulb rated at 75 watts or more. Try not use compact fluorescent or led lights as they don't draw the same amount of power compared to an incandescent light. If compact fluorescent lights are all you have, use the one that has the highest light output. Make sure the lamp and bulb work. Plug the lamp into the inverter. If it turns on, then the receiver is at fault, if the lamp does not come on, then its the inverter.
If the lamp does come on, but the light output is less than normal, then it could be either a power source or inverter problem.