One more thing is quite interesting is that when I don't switch off the button from the wall socket, I don't see this message at all.
Meaning when you turn off the plug at the wall socket and the pc has 0 power for any length of time, when you reapply power you get that message.
There's only 1 function of that tiny battery, that's to supply trickle power to the cmos chip which holds the variable bios information and settings. When you put power to the mother, pthe motherboard is supposed to disconnect the battery and takes over power regulation of the cmos. Like in a car, once it's started the alternator runs things, not the battery.
So I see one of 3 possible issues. You got given an old and mostly dead battery from that shelf. The motherboard is failing to switch over to pc power leaving the battery running full time or you have a power leak allowing the battery to drain when the plug is turned off.
I have a 3rd gen pc. It's almost 8 years old and contains the original battery that came with the motherboard. That's how little power the cmos actually requires.
I'd start with a new battery. They are cheap. It's a watch battery, you can get them anywhere, most drug stores have them, hardware stores, anybody who sells batteries usually has them. They are not specific to motherboards and if that shopkeeper sold you a used one off the shelf, that was pretty dirty business.
But I'd start with that and see how things go, because any further repair is pointless at this age, a newer motherboard platform will cost almost as much as trying to find an acceptable motherboard to fit your pc now. And will still be 8-9 years old and used. Very large gamble on capacitor lifespan.