I browsed your forums and was able to print/run the kenmore washer diagnostics on my ailing washer. Im almost convinced it IS the door switch, but want to confirm one nagging question. Origonal issue, washer will not spin, will agitate without issue, but not spin. ran the diagnostics and it WILL spin full speed with or without a load, I had to spin out the failed load. Now, im almost convinced it is the door switch, but when it spins in diagnostics, does it bypass/ignore the door switch state? Also, the diagnostics code i got was a 4 full flash/beep and 3 silent start light flashes.
Here's the repair manual for your model: 3.0 cu.ft. Horizontal Axis Front-Load Washer (Good & Better Models): www.applianceblog.com/manuals/5995413084_Washer_2004.pdf
You can run the diagnostics and see if an error code comes up, Read Page 10. You have the "GOOD" model(non-digital display). So an error code will be read with the flashing lights you count.
Here's how to test the door lock latch switch assembly:
Remove the door lock assembly and
measure the resistance of the PTC.
The PTC is the wax motor on the door lock assembly. You will need an ohm meter to test that.
If it reads 1500 ohms, then its fine, and the problem would be the control board.