A new battery can easily cost 150€, so I would want to avoid that.
I'm have a similar issue, my laptop won't charge past 84% for over a year now. Recently I completely drained the battery untill it auto swithced off, when I wanted to start the laptop again nothing happened. What I did was removing the battery and trying again with only cable: didn't work. I put the battery back in so I could send it in for repair, but decided to try one last time, and it worked! Weird. Maybe that's something you can try? I know it looks tricky to disassemble the laptop, but if you want I can give you some tips, I think we have almost the same model. I think these laptops are not really built to be used with battery only, I try to use power cable as much as possible.