[bakareika]

While an Orthodox Jew cannot directly ask you to take his cellphone and turn it on, he or she will be indifferent to you taking and power cycling it voluntarily. It's the intent and activity that's considered sinful, not state of the device per se.

Also it's perfectly normal to leave a phone powered on for a Sabbath, if you don't actively use it. Same applies to e.g. elevators, that just cruise in an endless loop and stop on every floor. You can ride in it, as long as you aren't the operator.

Source: living in Israel for many years.