It's not necessarily dangerous but lithium batteries have a chance to fail and in very rare cases even explode, making them a potential fire hazard. I'm not an expert, maybe someone else can expand on this. If I were to run an old laptop of unknown provenance with a LiIon battery 24/7 completely unattended I'd at least want to make sure that it is on a non-flammable surface without any flammable items nearby.
>In the past I used an HP DL380 Gen. 7 (which I still own, and wouldn't mind selling as I don't use it), but I had to find a solution for the noise. And power consumption was at around 18EUR for my EUR/kWh.
Yes, I am surprised how many people leave power consumption out of the equation. These days you can rent a decent VPS for the power cost of an old refurb server alone.