Its possible it could be the switch. Either get a new switch, or if you have crimps and a crimping tool handy, crimp the cables together without the switch.
(certainly dont put the live connectors together and very very tightly wrap it with insulation tape for a brief test fire...)
That motor doesnt sound like it is so cheap its dead on arrival. Thermal cutout is a module (usually white holding bracket and black square inside thst) that sits on the side of the motor near where the main wires come out.
If youve got the time and, avain, spare cable and crimps, strip her back to the motor, feed the new length of wire through the spine cable route and 2 female crimp it to the motor, pjt back together so it holds steady (can get away with just screwing the motor housing back together) incase it fires up and shoots across the room...
Either way, bypass the switch. The main cable wouldnt go unless its visibly damaged, and ive never known a dc14 to breal itself by the machine like the dc04s did!