Thanks for the detailed explanation.
I'm not an expert on laptops, my laptop is about 3-4 years old and
several days ago I had to replace it a hard disk and one of its
memories (128x2 MB), that suddenly stopped working. So, the battery has
suddenly become less important issue. Though, it still very anoying,
"charging 0%".

I was offered to buy a new battery or to recharge the old one, for half
price of the new one, but I'm not sure I want to invest more in this
laptop.
Any suggestions: new or recharge?