I would check carefully your soldering on / near pin 6 of the JP302 connector and its companion on the mother board.? Maybe there is a short to another node, or a 'cold' solder joint with resistance.
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As you have noted, the three buttons (excluding the power button) all use one electrical line with different resistances.? On the processor side of the connector, there is a 2.2k pull-up resistor to Vdd.? So when you press a button, it gives a voltage divider between 2.2k and the resistor value of the button.? The processor detects the divider voltage on its input pin with an internal A/D.? When no button is pressed, the processor sees the full-scale voltage.? The left button has the lowest resistance, so gives the lowest voltage to the processor, about 2/3 scale.? The right button gives a higher voltage, at about 3/4 scale .? And the right-encoder button gives a higher voltage still, about 7/8 scale.
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Since your processor is seeing a constant right-button when none are pressed, there is somehow getting a 6-8k resistance in the connectors/trace to the processor.? Pressing any button will put another resistance in parallel with that, causing a different voltage level, therefore a different button detection to the processor.
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Good luck finding the problem.? Shouldn't be too hard.
Stan KC7XE