Well, it gets more and more baffling.
Checked the bios. Identical on both machines.
Checked the switch settings. Identical.
Checked the WOL header. Nothing on either of them.
Swapped hard drives. The condition stays with the hardware, doesn't follow the drive.
Reset bios to defaults. Nothing changes. As it shouldn't, since I had previously reset it by removing the battery.
Gave up, and furiously put in another card, thinking, this should not be possible, I should be able to figure this out! Works fine on eth1.
Peter