I have just had my screen replaced on my HP Spectra, cracking machine (literally), it's 18 months old roughly and a known issue with the hinges causing the problem but HP still wanted £300 to replace.
Your checks are commendable but too comprehensive imo, I'd expect those on a monitored takeover.
Discuss the history of any issues, check bells, batteries (Inc current and charge) , induced ac at a push, walk test Inc pa's, cct resistance, brew.
The detector in the photo shows it the right way, but that casing is designed to mount the other way up, there will have been a small securing screw near the tab, hence the hole.
This is the train of thought with a lot of people sadly, when you turn up and your doors are swinging in the wind and your nice, expensive kit has gone the savings will pale into insignificance.