Have you tried removing and re-installing the lens? Do you have more than one lens? If so, try the camera with a second lens. Have you tested the battery with a battery tester? Although rare, sometimes even new batteries are not fully charged. Have you tried lightly abrading the battery contacts in the battery chamber with the rubber eraser of a pencil. If the contacts get even lightly corroded, the current can fail to flow, leaving the camera unusable.
If you had previously used the mirror lockup socket on the lens, if it isn’t fully retracted, the shutter won’t fire from the body’s shutter release. This is easy to remedy by fully installing a cable release into the release socket on the side of the lens, snugging it just a bit, and then unscrewing the cable. You should see the socket retract into the lens body as the cable is unscrewed. See page 29 & 30 in the manual for more information on the use of the mirror-up cable release socket on the side of the lens.
Firing the shutter in “emergency” mode for anything other than flash-only use is pointless. It simply mechanically releases the shutter at approximately 1/400 second.
I presume that you’ve checked page 39 “Troubleshooting” in the RZ67 manual. If not, check the items cited in the box on the right hand of the page.
https://www.focale22.com/pdf/rz67pro_instructions_manual.pdf
If you’ve done everything that’s listed, then you need to consult an experienced Mamiya technician—if you can find one. The RZ67 is far too complex for the average camera owner to deal with on his or her own.