This is dictation.
In general, this forum focuses on best software adjustments and updates and to a lesser extent on hardware troubleshooting. In general terms, most users did troubleshooting by means of substitution. In your case you would obtain an external charging system for that battery you have. From what you said, it would appear that you now have two good batteries and one laptop that will not charge the batteries. The logical thing is to get an external device for charging the batteries without any dependency on the laptop.
You can buy such devices from stores like new egg or Amazon and other sources.
Now if the moderator of this forum has the forbearance to put up with one of my rants and rambles, I will try to give a concise summary of something that most laymen do not get involved in. Statistical analysis of electronic component failures shows some general patterns and some exceptions to the general rules. Usually electronic components will fail within the first few hours or first few days of usage. However, there are some exceptions to this general rule. Sometimes these are called esoteric exceptions. Which just means that was very unexpected.
For example, electrolytic capacitors. They have a reputation for failures at unexpected times. In the manufacturing process some small companies that make electrolytic think they can get away with short-term testing and they release onto the market low-cost components that will not last a long period of time. This has been well documented elsewhere, I am not making this up.
To a lesser extent, other components can fail. These include Zener diodes, power transistors and linear voltage regulators. Additionally, there are more complex voltage regulator chips that because of their complexity can have an unknown failure rate.
Asked to motherboard failure, a component failure is also a motherboard failure if you don't know which component that is. If the component cannot be isolated, the technician will simply send the motherboard back to the factory and see if they can fix it. The common failures in the motherboard are bad solder joints and in some cases a broken trace. A trace could be broken by mishandling or simply by oxidation. During the manufacturing process something could happen to motherboard that will shorten its life. Motherboards are usually tested for a period of several hours or even days before they are shipped out to the companies that manufacture laptop computers. But even so, once in a while a rare thing will happen, the tested certified motherboard will fail after several months of use. Is that very rare? Yes, very rare. But if 20,000 motherboards were manufactured there is the possibility that at least a few will go bad.
The most common failure of charging system is the battery itself. But just because it's the most common problem does not translate into it always been the problem. I'm going to refer you to a link on Wikipedia that is in general a good coverage of the subject of electronic component failure.
https://en.wikipedia.org/wiki/Failure_of_electronic_componentsThanks to the moderator of the forum for letting me give a rather verbose explanation of how component failures can be very unexpected and unpredictable.