Thanks for the pics of your dearly deceased motor! So there's definately no sign of a mechanical switch?
I don't know much about motors but I think the links that you can see in the junction box are for reversing the motor rather than selecting the voltage. Infact, I know this because I wired up the reverse switch for mine so I could try cutting threads on the lathe. The leaflet that came with the motor describes what needs to be done. Pic attached.
Hmmm...I think I should start by testing the capacitor before I get too medieval on it's carcass.
Might try their parts & service phone number on Monday.