Well, as I said, it's not a big problem. This is just something I do for fun, find an abandoned camera and try to bring it to life. I'm probably going to donate it to my community college's photo program, telling them that it only works in manual and aperture-priority. But here is the observed behavior, step-by-step.
Set the camera to Program, set the lens (in this case, an AIs 25-50mm Nikkor) to f/22. Look at the display, it reads whatever shutter speed the dial is currently set to, and also displays the M and +/- signs as it is pointed at different light sources. At no point does the camera adjust the shutter speed the way it would if it was working in Program.
Set the camera to shutter-priority, set the lens to f/22. Point the camera at different light sources, and the shutter speed changes to provide an accurate exposure for the current aperture (f/22). You can set whatever shutter speed you like on the dial, and the camera ignores it; it seems to be working as if it was set to aperture-priority.
I've owned several Nikon FGs (which would be a great camera if it only had DOF preview, a sync socket, and exposure lock...). Anyway one of them had a similar issue; it worked fine in manual and aperture priority, but put it in P, and it would trip the mirror and then not open the shutter. You'd have to switch the shutter speed dial to any other setting to drop the mirror, and you'd lose that frame.