Here are a few Different models as i do not know yours.
How to Unlock the Control on Whirlpool Duet eHow
Maytag - To unlock the controls, press and hold the CYCLE END SIGNAL for 3 deliberate seconds or until the control lock light goes out. If the control locked light will not turn off, I recommend unplugging the washer for 5 minutes. Plug the unit back in and see if the controls will respond. If not, I recommend calling a service technician to diagnose and repair the washer. You could have a failed control console or a bad electronic control board in the washer.
Kemmore- Unplug for 10 minutes.
GE washer - Make sure that the control for the washer is not locked. If it is, press and hold the LOCK button for 3 deliberate seconds (or until the control unlocks).
There is not another way to reset the control board other than completely unplugging the washer as you have been doing. Since the display light up and works, the washer apparently has electrical power supplied to the control board and control console. You could have a failure in the console that is preventing the start button from working. A failed control board or a problem with the door switch could also prevent the washer from starting. Make sure that the washer door is firmly closed.
If the washer will not start after checking the control lock and the door, I recommend calling a service technician to diagnose and repair the washer.
Good luck More info would be helpful. Make and model. Is always a plus.