Good guess that you've got a failing board on your hands. Start removing NICs one by one. Reboot until you find the "odd man out," which will be the card that's in your hand.
Software goes apesh*t when
hardware goes apesh*t.
The reason why I'm saying that this is "undoubtedly a hardware problem" is that the system was working fine,
and that it was beginning to report network-card errors, and the
only thing that you did was reboot. Obviously the device-initialization code is encountering those same errors. (Did you happen to notice which card(s) it was complaining about? If not, use the process of elimination.)