Agitates fine on fast setting, but stops and starts on slow.

I believe this machine can operate without the foot pedal attached. Disconnect the foot pedal and try using Start/Stop button. If same symptoms with pedal detached then likely problem is speed control module inside machine.

have a look at this link might help.
washing machine agitates really slow Google Search

Sometimes things can get out of sync. Try unplugging the machine for a few hours to rest the code on the board. It's like rebooting your computer. I did this to mine and it cleared up the problem. The capacitors on the board need to discharge to completely depower the board. That why unplugging and replugging right away doesn't always work.

Check the IAC (idle air control) they get gumed up and are slow to operate.

sounds like the contacts in the timer are burned or siezed

this sounds ilke its in a delicate cycle or fabric care cycle...did you try putting this in normal or regular wash are the speed selectors set to fast/fast...let me know if this does not help...

Bad timer. Try to find a used one if possible, this item is a little expensive.

Check your speed selector switch (fast/slow, fast/fast, normal/fast etc.)first and foremost! Make sure it not set in-between speeds.
If it is ok then my nest bet is that the switch itself is bad.
If your machine does not have a speed selector switch, I'm afraid you may have a bad motor.
Good luck!!

Your motor/clutch combo is on the way out. The motor is overheating and turning off. Cools down and restarts.
You need a new motor/clutch combo or a new washer. I do not recommend another GE.

test the machine empty without clothes in it, if all is well then i think your problem may be the motor carbons, take them off and check for damage, make sure one of them has not spit down the middle, also look at the armature for signs of sparking,a worn armature or carbons will work fine at slow speeds

you haven't mentioned the carbons, its trying to spin so may not be the pcb