According to ctd4x4 :
Dumb question, but does Grainger sell exactly the same motor? Nutone
wants $360 for a new one. A completely new wholehouse fan can be had
from them for $350.

I know Nutone's model number for the motor (K8484000) and the specs:
2-speed, 1/3HP, 615 watts, 6.5 amps, 1725 RPM.

By all means, check out Graingers - it might be a moderately standard
form-factor motor (all you have to do is match HP, RPMs, voltage
mounting and speeds.).

Otherwise, getting it rebuilt may be a perfectly good option.

I had a Sears 1HP RAS motor go bad. Unique, now unobtainable motor.
Repair cost about $90 (including taxes).

HOWEVER,

Before doing either tho, I'd carefully run continuity/short tests of all the
wiring. Eg: breaker to switch, switch to motor, neutral-case etc.
Inspect the connections inside the motor. Inspect any wire that contractor
may have come in contact with.

While a hot-neutral short, say, would show itself by blowing a breaker,
it seems to me that, say, a short between the high and low leads could
lead to the motor humming and refusing to start. Check inside the motor's
junction box for something that slipped off/shorting an adjacent wire.

[Given what you're looking for, be _careful_ touching the motor housing
under power. Check for voltage on the case.]

Secondly, the starter contacts may be stuck. Give the motor case and shaft
end a couple good hard raps with a screwdriver handle or rubber mallet. Hard
enough to get its teeth rattling, but not enough to fracture its skull ;-)

If that fails to get it to start, you have nothing to lose by disassembling
the motor and checking contactors etc.

[Remember to kill the breaker of course.]
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.