Mac II, IIx, and IIfx all require both good batteries to turn on, either that or a jump start directly to the power supply. I am not aware of any single-battery Macs that need good batteries to turn on. The IIci and IIsi do not require a good battery. Some require an on-off-on sequence to turn on with a dead battery, such as all 610/660AV/6100 style Macs.

This is why I remove all batteries from all Macs, there is no sense risking an explosion when I can just work with the quirks and fix a few settings each time.