Do the drives turn on.? It's difficult to help without knowing how it's wired so what I'm trying to determine is if the e-stop is hard-wired and running through a relay that controls the whole system and then just sends a message to Mach3 that E-stop happened. Or if it's wired directly to the controller, in which case if the switch is ok it should reset.

If it's hard wired through a relay then you could have a dead relay or blown fuse which is stopping it power up so mach3 won't get the OK and won't reset. But also the drives won't power up or will power up so easy to spot.
A safe system would use such a setup and it fits with mach3 not coming out of reset if the E-stop switch is ok.

The other thing it could be is a broken wire on the E-stop loop so even thou the switch is ok the signal is still not getting thru. Check the E-stop loop at the BOB with a meter for continuity.

But Like I say it's difficult to tell you where to look without knowing more about how it's wired.

I presumed you've tried this but just in case close down the computer and restart. Not just Mach3. If you are using a parallel port then check the cable hasn't come out as well because mach3 could see this as charge pump failure and E-stop.