Hi @mzamobheki
You cannot repair batteries.
The best that you can do is either replace them or find out what the problem is on the motherboard if the battery is not charging or supplying power to the motherboard.
Here's the [https://download.lenovo.com/pccbbs/mobiles_pdf/b590_hmm_en.pdf|hardware maintenance manual] for the laptop.
Go to p.44 to view the procedure to replace the main battery.
Here is a list of all the batteries that are compatible with the laptop.
Battery, 6CELL 2.2Ah, 48Wh, Sanyo Part # 121500047 ''[br]
''Battery, 6CELL 2.2Ah, 48Wh, Sony Part # 121500048 [br]
Battery, 6CELL 2.2Ah, 48Wh, LG Part # 121500049 ''[br]
''Battery, 6CELL 2.2Ah, 48Wh, SMP Part # 121500050 [br]
Battery, 6CELL 2.8Ah, L11L6F01 3S2P 62Wh Batt C01 Origa, LG Part # 121500052 ''[br]
''Battery, 6CELL 2.8Ah, SM/S L11M6F01 3S2P 62Wh Batt C01 Origa, SMP Part # 121500053.
Search online using the ''part number only'' to find suppliers that suit you best.
Given the age of the laptop, if you haven't already done so I suggest that you check the voltage of the back up battery as well - see p.52. If it is <2.6V DC replace it. Usually it is a CR2032 3V Lithium coin cell battery which is commonly available everywhere e.g. supermarkets. The battery type number is printed on the battery itself, if you wish to verify what type it is.