This article describes the G52S LED behaviour. 

Off If the LED is not on at all, it is likely that the battery is flat, or that the device is asleep. Measure the battery voltage with a multimeter. If there is charge (above 3.5V), reset the device by removing and replacing the battery and solar panel.
From off, switches on briefly, and switches off again
Likely to mean the device is powering up, checking the battery level, and shutting down because it is too low. Check battery level.
Slow flash (10ms ever 2sec)
Running. Depending on the FW, could be getting a GPS fix, or powering up the modem.
Fast flash (10ms ever 0.5sec)
Connected to the server. Once the modem makes a successful connection to the server, the LED will flash fast.
Sending a record. While waiting for a commit response, the LED will stay on.
Very fast flash for 2 sec, followed by slow flash.
Firmware update. If the device receives new firmware, it will boot load to update itself. While updating, the LED will flash very fast. Once finished, it will start up normally and resume the slow flash.