You can get a multi-meter that will suit the task from the BORG-esques for $15-$20.
Unplug the saw.
Open the cover on the motor's electrical box and there should be 3 wires coming from the switch (2 hot and 1 ground). The hot wires may have wire nuts or bayonet-style connectors. Make sure that you can safely get the multi-meter's leads into contact with the hot wires, but not expose yourself to shock or short a hot to the frame. (You can disconnect the hot wires and leave them 'hanging' free, if necessary.)
Reconnect the saw's power plug. Press the start button. Use the multi-meter to measure voltage on the hot wires at the motor for 240V power. Also measure each hot to ground (120V).
Unplug, reconnect, and re-install covers as needed.
If you have 240V between the hot legs, the problem is in the motor.
If you don't have 240V (hot<>hot) and/or no 120V (both)(hot<>gnd), the problem is in the switch/starter/wiring.
It will be much easier to provide further assistance, once you have 'split' the potential problem sources in half.