Kenmore washer won't drain - all mechanical components are working

Might want to try hooking up the pump to an external power source that includes a switch so that the pump itself can be ruled out as intermittent; that is, hook it up, toggle the switch on and off several times in succession to see if the pump is energized each time. Unhook all connectors/terminals and clean/reseat. Check for any protection components (ie thermal) that may be malfunctioning. Continuity checks with unit unplugged, wiggling wires for making and breaking continuity etc. Some units will have a schematic included (maybe not always obvious location) that details what particular components are engaged via the logic board(s) when the unit is performing a particular action; might also show voltages which could be checked with multimeter.