check heater to ground, e6* are heat issues, and if it does it on start up. its prolly something in the heater circuit that is grounded.
crappy heater in that machine, the frame that holds the heater in place tends to warp, causing the heater to touch the heater housing.
if you find a grounded heater on these machines, after changing the heater, always run the machine on air fluff, just to ensure the contacts on the heater relay are not fused, seen it a few times already
it appears the heater thermostat is in series with the neutral line, check for a open heater circuit, rinse cycles dont heat water,all other cycles do, so this may be a cause for only rinse running the wash motor
this manual is for both mechanical controls and the lovely genesis controls you have
you say the freezer is cold and you can feel a fan blowing into the FF compartment?
cause really,you should have cooling in the FF section then. unless.... something is blocking the return air vent behind the bottom crisper,remove that crisper and make sure nothing has fallen down there blocking the return vent(the fan will "blow" with the doors open, but soon as the doors are closed,the fan will not be able to circulate air between the 2 compartments
after that i'd be looking for proper damper operation
that manual page is open for public viewing and contains most older friggy manuals if you ever need one again
first thing you can do is remove the lid and back panel, there will be a tech sheet either on the top of the dispensor,or taped to the inside of the cabinet
try to run the diagnostics
carefull around the opening of the back panel, its very sharp
also.... while behind the machine with back panel off, grasp tub and rock it towards the white motor board, watch to see if the tub can come into contact with any of the wining harness,inspect that harness very closely looking for broken or crushed wires(the fine wires can get crushed,the wire breaks inside the insulation)