A couple of circuit diagrams may help.
1) From the manual. I’ve marked the current flow and components to be checked in red. Note these may not exactly match your lathe – they vary a bit,

Simplified:

The fuse must be OK because the lathe runs when the NVR is pressed.
Pressing the NVR connects power to a relay inside the switch via the e-stop, chuck guard, gear cover interlocks and the Forward Reverse switch,
Not unusual for the NVR switch to fail, faulty relay coil or contacts. Replace it, (already done)
Make sure the e-stop is released. They usually lock when pressed, and are reactivated by turning the mushroom. It has arrows on top.
The lathe won’t operate if the gear cover is off. Not a switch in the ordinary sense. A blade enters a slot,
I had trouble with my chuck guard switch. Came loose and twisted so that moving the cover didn’t operate the switch. Fixed by putting the switch back in place and re tightening.
Check all the wires are connected; they can vibrate loose.
If that doesn’t work, buy a multimeter and trace the circuit continuity end to end. The lathe won’t start unless all the safety switches are close open, or if a wire isn’t connected. The symptoms are as described.
It will be easy enough to fix once the fault is identified. Judging by the lack of complaints, unlikely to be the F/R switch.
Dave