Some of the cycle selection buttons don't work at all (e.g., Econowash). Other buttons work only after pressing several times. What repair part do I need?

You do not seem to be getting an answer, so I will give it a shot.
The original poster may still jump in but in the mean time some is better than none.

I a cannot find a control panel (keypad) schematic so cannot help with you testing it for continuity.

You may want to try the following. On most units a number of keys will use a common track on the ribbon cable. If this track cracks or makes a poor connection you loose a number of keys usually 3 or 4.

Connector Cleaning / Checking
Unplug the unit
Open it up
Remove the ribbon cable from the keypad to the control board at the control board.
Clean the edge connector.
If it is the type where there is not a connector just the insulation is removed, it can be cleaned with a pencil eraser. Do not use an ink eraser as it is too abrasive.
Check the tracks in the ribbon cable for hairline cracks. A magnifying glass helps here.
Would not hurt to clean the connector on the board. Use electronics contact cleaner or isopropyl alcohol and a tooth brush. Be gentle and do not reconnect till all the solvent evaporates.
Reconnect everything and give it a try.