if you want to move it onto another image, it's easier to just copy and paste. Ctrl-A, Ctrl-C, then on the new image Ctrl-V to paste as a new layer. If turning off the Auto-select option helps, then that's fine (or just hold Ctrl while using the Move Tool to turn it off temporarily), and drag it over. Sometimes even then the Move Tool can't "see" the item.
Another option is to make a new layer under the transparent thing, link the two layers, and move as a group. Then just click the eye on the other layer.
The Arrow keys are great for moving around on the same layout/image as Dodie suggested, remember that Shift-arrow moves it a chunk rather than nudging it a little
SELLING MY SIGMA NIKON F 10-20mm f/4-5.6 ULTRA WIDE-ANGLE LENS