The camera is behaving the same as if there is no battery at all installed.
Since the battery is good and the lens works on other bodies, perhaps
- the contacts in the on-off switch are not connecting, so timing circuit is not energized
- the rotary speed selection dial is not connecting, so no chosen speed is set and the lens defaults to 1/500
- the electronic timing circuit is toast
Do you see the red shutter-closing indicator in the viewfinder at all? Any of the above can account for no indicator
When you press the battery check button, does the indicator light? If not, the on-off switch is not closing.