Start with the basic troubleshooting tips on page 18 of the Owner’s Manual (link below). For “Washer won’t spin” the manual says the possible causes are 1. Washer door is open, 2. Dispenser drawer is open, and/or 3. Load is too small.
Next, check if the washer is giving off an error code . Essentially, if an error code occurs, the lights will flash and it will beep a number of times. The number of flashes is the error code. Then, it will pause for two seconds, and then repeat the error code. See page 23 of the Service Manual below for deciphering the error code.
Next, go to page 7 of the Service Manual. Perform the diagnostic test. You’re most interested in paragraph 9 for the spin cycle. This will manually put the washer into spin, and perhaps throw an error code for you to diagnose.
Finally, go to page 26 and perform test 9.
Most likely, you problem is either the door switch assembly (see pages 12-13), the inverter or the motor (see page 21). Hopefully, you will have a clear error code. If not, test 9 on page 26 will be your guide.
# REF - Owner’s Manual: https://data2.manualslib.com/pdf/6/597/59672-ge/wssh300.pdf?d2f8a489145f9458d3c90f0629442037
# REF - Service Manual: https://data2.manualslib.com/pdf3/78/7729/772841-ge/wssh300g.pdf?8fa300f38ca93cbe571559187c6bed1e