So, BusyBee suspects it may be the capacitor, if the motor can run once spun up. They don't have any available, but provided the specs below:
Hello Andrew,
The capacitor is not in stock currently.
You can source it locally.
Specs are:
200 micro farad, 150 VAC, 2 3/4" x 1 5/8".
There isn't a whole lot available locally for that, but Grainger has a 190-227uF and 165VAC cap for sale that can arrive within a week (Here) . Its a slightly different dimension than the specs, physically and electrically, but we can probably make it fit. Otherwise, I can look further afield to overseas shipping, or if anyone knows where it town we might be able to find one.
If that fails, the entire motor can be ordered from BusyBee for around $210.