I had a similar problem with my Edge. First thing I did was put it on the charger and it still didn't turn on. Next thing I did was fiddle with the battery release mechanism and try to reseat the battery. Then suddenly it powered up again and my Edge was working again. So definitely check if your battery is properly seated. I guess I was playing the battery release to see how easily was to change batteries, and I did not lock the battery in place. That did it for me.

Henry