Down in my den which is half below grade, the phone signal isn't very strong. In inclement weather I sometimes have just a hint of a bar on the signal meter. I noticed a few nightes ago that when the 650 did one of those mysterious "turn ons for no reason" where the screen and keyboard lights up, that the LED was also blinking and looking at the phone screen it was searching for the network.
I wonder now if the one source of the turn ons isn't the Treo looking for a new tower as one travels out of a cell and temporaily lost signal. It never turns on by itself when phone is off, at least not that I have noticed.