Brew light off before shot completion.

This does not indicate a problem with the machine. The green light turns on (and the heating element turns off) when the boiler has reached brew temp (127C/260F). When you press the brew button, the pump turns on and pressurizes the system enough to push hot water out of the boiler and through the portafilter, at the same time drawing room-temperature water from the tank to replenish the boiler. As you might imagine, this has the effect of gradually lowering the boiler temperature until the lower-limit thermostat trips (95C/203F), turning the ready light off and the heating element back on. The temperature of the boiler will constantly bounce between these temperatures any time it's on; running the pump simply speeds up the trip across the range.

I hope that isn't too confusing, in short, your machine is working as designed :)