Gfci open hot but trip indicator lit
The GFCI receptacle has power on the LINE side, and that is where the status lights are powered from.  The GFCI is in tripped mode, which means no power comes through to the LOAD side, which includes the sockets on the face of the GFCI and anything attached to the LOAD screws.  

Troubleshooting the GFCI

First, it's rarely the GFCI. But let's exclude it anyway.  To do this, we must isolate the GFCI.  That means we must remove all wires from the LOAD terminals of the GFCI - all of them, don't go thinking you can leave neutral.  

Now, with absolutely nothing on LOAD, the GFCI should run through its paces.  It should reset, and Test should trip it.  The magic 8-ball tester's GFCI function should also trip it if it is grounded (otherwise it's supposed to not trip, don't try to modify the GFCI's wiring so it does).  

Does the GFCI refuse to behave with nothing plugged in and nothing on LOAD? Then it is the GFCI.  Otherwise, it is not, and never was.

If the GFCI isn't bad, the downline wiring is

People have a dreadful habit of using the LOAD terminals merely as extra screws to put on more wires.  Never do this.  If you don't  understand what LOAD actually does, don't  use it.  If you don't actually intend to protect the downline, don't use it.   Move those wires to LINE and leave the warning tape on LOAD.  

However, it is a fact that your downline wiring has a problem.  Moving it to LINE would mask that problem.  So you may want to leave it on LOAD and actually fix the problem.  


To start, unplug everything plugged into that part of the circuit.  If that solves it, then an appliance has a ground fault. Plug them into kitchen GFCIs one at a time until you find the one tripping GFCIs. 
it may be a wiring problem where a wire (possibly neutral) is faulting to ground.  That can happen in crowded boxes where a ground wire kisses a neutral terminal.   Or in metal boxes where the receptacle or switch is pressing against the side of the box.  
it may be mis-wiring, typically with shared/borrowed neutrals, or one of several mistakes that can happen when a switch is in the same box with the GFCI.  If this is the first time installing a GFCI here, this is likely the case.