The shutter time in regular mode is electronically governed. It cannot be used (won't release) without a battery present, in good condition, and properly oriented. The RZ67 has a number of exposure-prevention interlocks so that you don’t waste film when something is not in correct shooting mode. It’s most likely that one of the “DON’T FIRE” conditions is correctly preventing you from shooting. See the “MONITOR LAMPS” warnings on page 16 of the manual.
For example, the dark slide must not be in the slot at the front of the film holder. Otherwise, you’d waste a frame of film (unexposed). The battery must be fresh and installed in the correct orientation.
Here’s the manual, enlarge the view as necessary:
http://www.mamiyaleaf.com/assets/files/documentation/RZ67_Pro_v4.pdf
The cardinal rule for the RZ67 or any other sophisticated equipment: “
When in doubt—READ THE MANUAL.”
Whenever you don’t plan on using it for 2 weeks or longer, it’s prudent to remove the battery so that the contacts won’t get ruined by corrosion due to a leaking battery.