The backup battery is powerful enough to maintain a powerbook in sleep mode for as much as a couple of days; they are rather robust when functional, in other words. The way the power settings are programmed to work, furthermore, is that the machine expects there to be reserve power when the main battery runs out of juice, so that the machine automatically goes to sleep and switches to the backup cells. On some models, it is true, it appears that a dead backup battery has relatively little effect, beyond the loss of pram settings on removal of power. On others, including at least some Pismos, a dead backup battery can cause an anomalous refusal to do anything at all when the attempt is made to power on. It is standard practice in reviving a "dead" Pismo, therefore, simply to disconnect the leads of a dead/ discharged backup battery as the first step in diagnosis and recovery, since it is common experience that a supposedly "dead" machine will power up once the source of the trouble (the backup battery) is removed. Many "dead" Pismos one finds listed on eBay are not dead at all, and many are new enough to have perfectly functional backup cells that just need a little TLC to be revived. My Pismo came to me in just this state.

It would seem from this that the Power Management subsystem relies on those backup cells, or at least, that it can be easily corrupted without their being in working condition. Why these Pismos will start up with no backup battery at all is anyone's guess: residual power that just confuses matters, perchance?

I have in the past had some duplicate Duos, some with functional backup batteries and some without; those with functional backup batteries were (and are) rock solid machines, whereas those without have behaved erratically. You could boot one of them, but in use there could be anything from random shutdowns to episodic GLOD to refusals to reboot and so regular reset requirements to deal with. All this is best avoided, unless all you want is to tinker with a machine once a year when taken off a dusty shelf.

There are some characteristically informed posts around and about from equill on this subject, as I recall, that might be ferrited out for reference. There are also some useful posts on Apple's Support/ Discussion pages and other sites such as the old Duolist that appear when GLOD is researched.