I have a laptop from 2011-2013 so about the hang. At that time it already had an SSD. Despite the new battery, the battery life is extremely modest. I put Linux on it to test it just for fun. Unfortunately it is not satisfactory because it completely loses its portability due to the limited battery life and because I don't want to have this tangle of cables in the living room it just looks stupid now.
Could I give this laptop some other useful job? If yes, which?
A new (replica) battery doesn't cost the world if you had a use for a (mobile) laptop. For work, I also use a laptop that is even older (from 2009-2010), albeit with 8GB RAM and an SSD.
Why don't you just remove the battery and just go over the network? - By the way, the notebook on which I'm writing this is from 2009!
As I said, I installed a new battery. Unfortunately, not much changes in the running time. 2 hours and it's empty. Then I exchanged the entire charging cable, no change. It also loses battery power when the laptop is shut down and switched off. If you let it rest for 2 weeks and want to switch it on, the battery is empty by itself, even though it is new
Because I don't want the cable tangle
I would buy a new battery. If that is not possible, you can leave it on the network and set it up stationary. E.g. On the TV to watch Netflix or as a display for pictures at celebrations, etc.
How long was the running time when the Labbi was new?
I do not know that anymore. Not particularly long either, but longer than maybe 4-5 hours now