Did you ever have a remote for the CD player, and if so, was there a POWER button on it? I also have a Sony CD player but it came without a remote, and you are correct, there isn't a POWER button, it appears that the unit was designed to only be turned off at the device. This is not uncommon as many manufacturers also include a power outlet on the back of their receivers so that you can turn on the receiver and the rest of the gear turns on too.

Rob.
http://www.hifi-remote.com/