I had exactly the same issue with my BH600G before I bought it. The short answer was a loose connection in the control box. After tightening all the screws on the contactors the motor started up normally.
First are you sure it is the motor, when applying power to the lathe, if all the safety switches are closed you get a clunk as the main contactor closes. No clunk then a safety switch is open. There is a small hum from the 24V transformer all the time.
If I remember right (ref pg 65 of Grizzly manual) the problem was the overload contactor FR had worked its way loose from KM1 (top left)
FR hangs under KM1 and is held in place by being screwed into T1, T2 and T3 on KM1.
In normal operation K3 (top right) closes, then for Fwd/Rev KM1 OR KM2 close. For testing, it is possible to push the centre of KM1 OR KM2 and start the motor.
The motor has connections U1, U2, V1 and V2. In the control box U1 = Neutral and on KM1 T1 = U2, T2 = V1 and T3 = V2
When running Fwd
U2 = Live
V1 = Neutral
V2 = Live
When running Rev, V1 and V2 are reversed.
U2 = Live
V1 = Live
V2 = Neutral
BTW It does not like starting from cold at a high spindle speed, releasing the belt tensioner lets the motor spin up to speed first.
Hope it helps
Adrian