New GFCI’s indicator light is green but outlets have no power
I have found many new models require the test and then reset buttons need to be pressed to activate the outlet and taped terminals. I would try pressing the test button then the reset sometimes these can be stiff but give that a try , if it doesn’t work provide the model # and brand.

Added after update, your radio works that helps, when you plug in the water heater the radio quits but you have power indicated with a non contact tester, this points to a loose neutral some place in the circuit. 

A radio may only take a few milliamperes of current so it works, but add a large load and now nothing is working but you have a voltage but there is no return path to complete the circuit with a heavy load, check that any pigtails on the neutral all the wires are tight pull on each one (one might pull out) verify at any other junctions , other outlets for the same but it will be on the neutral because you have voltage with a load.