Presumably the orange OD indicator remains out (off) during all this. And presumably the OD indicator responds properly to the pushbutton. If so, then it says that the signal from button to relay is OK.

A good electrical diagnostic is to monitor the wire at the solenoid. Look for the presence of 12 volts anytime the ignition's on and the orange OD light's out. When you push the button (and the light illuminates) the 12 volts should disappear. If you have 12 volts while you drive but OD remains off, then it suggests that the solenoid is not working properly. A good test is to swap it with a known good solenoid. Obviously, you could have problems deeper in the tranny -- but 90% of the time the problem's external and related to wiring, the relay, solenoid, bad ground, etc.

Since your tranny operates normally 1-2-3........ When under light throttle, are the shifts smooth and soft and at the correct engine speeds? If so, it means the kick-down cable is working properly. But if the 1-2-3 shifts are high and hard, it suggests that the cable is jammed fully out. This will interfer with proper shifts into OD.

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Don Foster (near Cape Cod, MA)