Chosen Solution
Hello guys! Big thanks for your support in advance! The problem first came when I had old battery (2000cycles), the macbook was working from Power source but showed Battery not charging (also neither green or red light were present on adapter). I tried resetting SMC, then replaced power adapter, then battery (at some point it was charging for about an hour, but then stopped again) and finally I/O board. But nothing changed - Macbook still not charging, but sees Power Adapter and works on it. What else can I try?
Sadly your battery has died! The battery is only designed to run through so many cycles! The expected limit is 1000 not 2000 as you can see here Determine battery cycle count for Mac notebooks So the first thing we need to do is replace the battery for sure! But before we do that lets check to see if the charging logic is healthy as your MagSafe charger LED should be lit at least Amber. Lets install this app CoconutBattery it will allow us to see the battery and the charging wattage. Post a snapshot of the main window so we can see Adding images to an existing question In addition, lets make sure your MagSafe charger is in good shape as well. Review this Apple T/N Apple Portables: Troubleshooting MagSafe adapters. Make sure the cord is not damaged and the contact surfaces of the MagSafe connector on both sides are clean and in good shape. Lastly make sure you have the correct charger and its a real one not a fake! OEM MagSafe Chargers vs Cheap Imposters: Teardown for Truth