Thanks. The strange thing is that my data connection is turned off; my roaming has never been turned on; and my wifi is turned off. Yet, even with that the Canadian Rogers still pops up with the white triangle. The only way to get around that is to turn my phone on airplane mode, in addition to the other things above. Even in airplane mode, the rectangle with the horizontal lines remains. And, the battery will still completely drain, even in airplane mode.
