Hi @uvfvb50vflmba
Manually getting a thermostat to operate/release may be different to if it does it automatically so to speak.
By "...if I play with the thermostat the motor kicks in." you mean just tapping it then replacing the thermostat might be a good idea.
The Danby part # is 1.03.02.01.070. If you search online for ''Danby 1.03.02.01.070'' you will get results for suppliers. Most say out of stock or no longer available, although depending on your location, I did find a [https://www.reliableparts.ca/product/inv_11461717|Canadian supplier] who has them in stock and also a [https://encompass.com/item/10272767/Danby/1.03.02.01.070/|US supplier] who can get one by early May.
If you need more parts here's the [https://www.danbyapplianceparts.ca/product-category/freezers/duf808we/|parts list] for the model.