The "VCR" mode is the mode you would use to play back footage that you've already recorded to the video tape, regardless of whether the camcorder is connected to anything. Generally on Sony camcorders there is a selector switch (with a little green lock button) that you use to turn the camcorder on, and it flips in two directions: the one direction turns the camcorder on and ready to record, and the other direction would set it to playback mode.
Also, all Sony mini DV camcorders that I am aware of do have Firewire ports, so check carefully again. The port will be tiny, and sort of W-shaped. Sony calls it iLink.