PM sent. Let it charge at least 4 hours. It still could have a capacity and internal drop problem, but a full charge will give it the best chance of running the machine. My understanding is that the gas gauge inside the battery is not to be trusted even a little until it has cycled thru a full discharge to sleep followed by a full recharge to 100%. But that it increased one or more LEDs seems to me to speak well about the laptop power board (but what do I know!). It's possible that recognition will not begin until the 100% point is reached also.
I'm running 10.3.9 on my Pismo with good PRAM battery and empty main battery compartment most of the time. You would think I should get a power adapter symbol with no battery outline but NO, I get a battery symbol outline with a bold X inside, this is true using both the YoYo style adapter and the PB1400 M4896 AC adapter. When I stick in a half charged M7318 battery the symbol changes to the battery with the plug adapter inside and (percent estimated charge) to the right. A few seconds later the battery changes to the battery outline with the squiggle ~ inside it indicating charging from AC adapter, the gas gauge number creeps up very, very slowly, 3 hrs plus to charge. When charging completes I think the symbol goes back to the battery outline with the plug adapter provided the battery remains inserted. When the battery is removed the outline with the bold X comes back almost immediately and the (percentage estimate) to the right goes away. There is an option to display the icon only, percentage gas gauge, or estimated time remaining-I have mine set to percentage.
It's possible something inside your laptop is bad causing sleep at the slightest voltage drop, but I think it is far more likely that you have misbehaving, possibly stale batteries, even the new one is suspect. It could be cell aging, or a malfunctioning smart monitor inside the battery that is shutting the battery down from inside. And as there are fewer and fewer G3 battery buyers, the quality of the warehouse stock of premanufactured G3 PowerBook batteries is going to be increasingly suspect due to aging.