When I looked at the battery icon for a lightning bolt I found what looks like an electric plug inside. When I unplugged the inside of the battery went dark. Easier to see than a lightning bolt. Once the charge went down to 99% i plugged back in and the little plug inside the battery came back. The little light on the end of the cord is still green, but the display often shows a rarge of 99%/100%. I'm pretty sure that light turns orange when its charging and green when it's finished.
The plug is likely due to you using the older macOS version. I am using 10.10.x. My (admittedly fuzzy) memory does seem to recall that older versions used the little plug symbol rather than the lightning bolt symbol. I no longer have a Mac running 10.6, so I cannot verify it.
I fell asleep last night waiting for an upload to Mega to finish and the computer was still saying 100% this morning so the cord is still working. The next time we have a long thunderstorm I'll see how long it takes the battery to drop its charge. We are supposed to have thunderstorms again today. Windows used to have a Power Manager that reported on the health of the battery. I haven't found anything like that in the drop down menu from the battery or preferences.
The icons on the menu bar are so small I'm always squinting at them. I have to get really close to see them clearly. So I simply remembered wrong - that the electric plug was inside the battery icon rather than replacing it. And panicked because now is no time for me to replace a battery or cord. I'm doing that a lot these days. Being in Legal Hockeysticks is killing me while the bad lawyers and bankers just get richer.
At a minimum, you should be able to go to the System Information app (or whatever it is called for 10.6...don't recall). It should have a section on Power that will give some health information about the battery. To do that, go to the Apple menu and select "About This Mac...". There should be a button that says "More info..." if memory serves (on newer versions, like what I am running, it is a button that says "System Report..."). That button will get you a window that lists a bunch of things along the left side. One of those items should be Power or something similar. There should then be a second on battery health.
There are also third party utilities. One is coconutBattery:http://www.coconut-flavour.com/coconutbattery/
They still offer a download of a version for macOS 10.6 (version 2.8 of the software is for 10.6...you will find the link for it towards the bottom of the page). There are likely other options out there, but I have actually used coconutBattery.