You don't say what make of sat nav you are using, but assuming that it is a tomtom similar to mine, the green light indicates that the unit is being charged ie connected to the cig lighter or similar.
Try pressing the on button for about ten seconds and see if that does it, or reset the unit. the reset is more complicated - turn the unit over and underneath you will see a tiny hole helpfully labelled reset in equally tiny lettering. Carefully push the end of a paper clip thru hole and push (not too hard!!) against the resistance you will feel.
If that gets the unit on its feet again - excellent - if not then I cannot help you any further.
Cheers
Peter
Peter Taylor, August 2009