This model is on the list of models that are prone to a sagging front apron that causes the bottom of the motor bracket to hit the bottom of the washer. Take the front panel off and observe under the motor to see if this is what is happening. If so, you will need a front apron bracket service kit. Complain to GE and you might get it at no cost.
For anyone interested in the theory. The motor in question is a single phase squirrel cage induction motor. A rotating magnetic field is required to get the rotor rotating. Single phase power does not provide this so we add another winding, the start winding. The way it is wound (number of turns and wire size) in conjunction with the series capacitor provides a phase shift in the current applied to it with respect to the current applied to the run winding. This creates a rotating magnetic field. Once the rotor is rotating, it creates its own rotating magnetic field and the start winding is no longer required and is switched out of circuit. On this particular motor, the start winding and capacitor are not designed for continuous power and will be damaged if not switched out of circuit after the motor starts or if it doesn't start. Starting direction of rotation is determined by the polarity of current through one winding with respect to the other winding. Reversing polarity of either winding will cause direction of rotation to reverse.
There is only one start winding which is for the high speed winding. There is no start winding for the low speed winding which is why the motor always starts in high speed even when low speed is selected. That's what one set of switch contacts is for. When low speed is selected, it starts in high speed via the switch contact but once the motor comes up to speed power is transfered to the low speed winding via the switch which is operated by the centrifugal mechanism in the motor. When high speed is selected, power is direct to the high speed winding. It doesn't go through any switch contacts.
If the low speed winding is open, if low speed was selected, the motor would continuously start/stop due to the centrifugal switch. This would not happen when high speed is selected as it doesn't go through any contacts. If the high speed winding was open, the motor wouldn't attempt to start regardless of speed selected. Power must be applied to both high speed winding and start winding in order for the motor to attempt to start.
It's not working in high speed motor function during agitation. Does it spin ok in normal cycles? If so, looks like a bad timer. If not, check the blue wire at the motor connector and timer connector. If blue wire connections and continuity check are good, bad timer.
It's called regenerative braking. When spin stops, the motor is used as a generator which causes it to slow down very quickly. The power generated by the motor in this mode has to be dealt with, so it is dumped into the high power resistor to be dissipated as heat. If the basket stops faster when lid is opened as opposed to normal end of cycle (lid closed), then yes, this may be what causes these resistors to fail. The new motors don't have the resistor so another method is being used to deal with the regenerated power.
Yes, if brake resistor is faulty, spin speed is limited to 50rpm. You can take the drip shield loose from the motor and check the resistor connections. Resistor is embedded inside the drip shield. Make sure washer is unplugged!
A faulty mode shifter coil would not prevent the machine from working. Go ahead and check it anyway to make sure you don't have multiple problems though. Unplug the 2 conductor plug and check resistance across the red and yellow wires. Should read around 98 ohms or around 65 ohms depending on version of shifter. On inverters with the red LED, you must lift a flap on the right side of the drip shield to see it.
If you have the new style of motor/inverter, the drip shield covers the front of the circuit board.
The 120vac should be there anytime the washer is plugged in. It doesn't make sense that you read good continuity but don't have 120vac there even when unplugged (no load on circuit). Yes, it is the far left plug. If you don't have power there you won't see the error code LED.
Re-reading your post, I see you did not check continuity between power plug hot and red/black at motor connector.
The only thing between the power plug and inverter board C2 plug are the line filter, fuse, and lid switch. Did you check the 120vac at the C2 connector with that connector plugged in or not? Try checking both ways. With it unplugged, based on your continuity checks, you should have 120vac there.
This is a very common problem with these washers. Either live with the squeel or replace the brake rotor. Access is from bottom of machine although we generally replace the snubber ring as well which requires removing the whole tub assembly. Brake rotor is under 200lbs of spring pressure and there is a special tool for taking the brake apart but there is another method. To get to the brake, you must remove the pulley and thrust washer. Then remove two screws from brake stator. Replace with 1 1/2" 10-24 screws. Now remove all the other screws and then slowly back off the 10-24 screws a little at a time each until spring pressure is relieved. Now you can clean the stator and replace the rotor.
I don't know, you never said if it agitates or not or if you checked for the loose nut. If it agitates, the motor is working regardless of the bad capacitor. Just replace the capacitor for now and check for the loose nut while your under there. You must perform the calibration function after you replace the capacitor.