I finally tried to switch controllers and to unplug other drives. Sorry for the delay of my reply: I have been away from the computer and I couldn't try earlier. Unfortunately, the drive is not recognized by any controller and the message viaide1: autoconfiguration error: BSY never cleared, status 0x80
changes to viaide[0123] depending on the controller I connected the drive to.
I also tried to install from a CD-R and remove the USB stick. Nothing changes.
However, I booted FreeBSD on the computer and I noticed that the disks are recognized as follows:
ada0 at ata3 bus 0 scbus3 target 0 lun 0
ada0: <ST3250620AS 3.AAK> ATA-7 SATA 1.x device
ada0: Serial Number 6QF2YYKG
ada0: 150.000MB/s transfers (SATA 1.x, UDMA5, PIO 8192bytes)
ada0: 238475MB (488397168 512 byte sectors)
ada1 at ata4 bus 0 scbus4 target 0 lun 0
ada1: <ST1000DM010-2EP102 CC43> ATA8-ACS SATA 3.x device
ada1: Serial Number ZN1CCXCF
ada1: 300.000MB/s transfers (SATA 2.x, UDMA5, PIO 8192bytes)
ada1: 953869MB (1953525168 512 byte sectors)
ada1: quirks=0x1<4K>
ada2 at ata6 bus 0 scbus6 target 0 lun 0
ada2: <ST3500418AS CC34> ATA8-ACS SATA 2.x device
ada2: Serial Number 6VM0D0EG
ada2: 300.000MB/s transfers (SATA 2.x, UDMA5, PIO 8192bytes)
ada2: 476940MB (976773168 512 byte sectors)
ada3 at ata7 bus 0 scbus7 target 0 lun 0
ada3: <WDC WD3200AAKS-00L9A0 01.03E01> ATA8-ACS SATA 2.x device
ada3: Serial Number WD-WCAV2D245516
ada3: 300.000MB/s transfers (SATA 2.x, UDMA5, PIO 8192bytes)
ada3: 305245MB (625142448 512 byte sectors)
Only the disk which is not recognized by NetBSD prints the "quirks" line. Do you deem possible that the "quirk" might be the cause of the problem with NetBSD? If so, I should try to understand what this 4K quirk means and how FreeBSD copes with it. Unfortunately ada(5) man page is not much helpful.
EDIT: The link above expired; I uploaded it again and added the output from FreeBSD. This is the new link: https://filebin.net/q8fie6bcgdtb5ok6