Try booting into Internet Recovery Mode using Command + Option + R since using just Command + R may be trying to load from the local recovery partition/volume.
Do you ever boot into the online installer to access the utilities screen? I just want to confirm if the process stops before this or after you actually select the "Install macOS" option.
Are there any error messages displayed?
Try power cycling your router and wait at least five minutes for the router to finish booting before trying again.
Otherwise you can create a bootable macOS USB installer using another Mac which is compatible with an OS this "broken" Mac can use. You first need to determine the exact model of this Mac so we know which versions of macOS are compatible. You can get the exact model by entering the system serial number on the check coverage page here (please don't post the serial number on the forum since it is considered personal information):
Check Your Service and Support Coverage - Apple Support