Short the electrodes together with some metallic object in a dim room to get an idea of how bright the LED should be. If the LED is dimmer than that when the electrodes are placed in the water, the water is pure enough. If the LED is nearly invisible..the water is EXTREMLY pure and it could take quite a while for things to get started.

If the generator shuts down well before it should or the LED brightens up to full when the electrodes are only a little bit submerged, the water is not pure enough.