In the EU, there's a _seller_ obligation for 2 years for items in the same class as laptop to ensure they are free from defects and fit for purpose. It won't help you if _you_ break your laptop, and after 6 months the burden of proof in the event of a dispute switches from the seller to the buyer, but I feel like pretty much all the issues the OP encountered would be covered under this.

A lot of add on warranties don't cover much more than this anyway, which makes them much harder to justify here.