The TTL prism of the Pentax 67 is powered by the 6v battery in the 67/6x7 body; the prism does not have a battery of its own, even in the absence or presence of an on/off switch (later versions of the TTL prism [1991->) have a discretionary on/off switch that also switches off by itself after 20 secs).
The battery will last around 10-15,000 exposures with a moderate amount of bulb/MLU exposures (be it noted that the 67 or 6x7 is a poor choice for extended bulb exposures as the mechanism employed — magnetic solenoids to hold the mirror up under MLU — is a heavy drain on the battery). Examine the contacts in the battery compartment, the contacts on the base of the prism and those on the camera. The 4xSR44 silver oxide batteries you speak of do not last as long as the single 6v A544/4LR44 battery. Further, one set will last about 5 hours with MLU or bulb operation. An alkaline battery should be used; it is no crime to go from silver oxide to alkaline or even a nuclear fuel pellet e.g borrow one from Curiosity on Mars...
I assume meter is actually reading a scene and not reading "dead" (needle persistently at bottom)? Just a check as not observing mount/dismount and remount process of lens and prism can result in the meter coupling pin not engaging and thus causing the meter to remain on indefinitely. A shorting of the shutter speed resistors that govern shutter speeds is also a possibility. If a changeover of batteries does not show an improvement, I think a bench examination of the entire camera is warranted, particularly if it is quite old, and all of the 67 and 6x7 bodies are getting on now, but still some beautiful little used specimens about.