Several possible ways to address this issue:
1. Check the LCD's menus for a "power on restore"-type setting.
2. Use a toothpick or small screw to wedge the LCD power button so it is always pressed. (works on some models, not on others)
3. Wire a switch in parallel with the LCD power switch.
3a Wire a switch in parallel with the LCD power switch and plug the LCD into the master slot of a smart strip. (preferably one with a sensitivity adjustment screw like the Smart Strip brand ones have IIRC)
Scott