I'm a running a small home network for a year and half using very old and crappy 486dx as a router. After some bad weather with lightning struck within 200m, the box stopped servicing. Due to some repairing on the power supply I even had to switch is off completely. After reboot the external network connection keeps failing.

Connecting a single client on the external net works fine. The internal net is still working. The external network card sends DHCP offers but simply doesn't get a lease.

Basicly that is wrong. I should be able to boot without changing settings. However I tried stopping the firewall: no effect. I checked if modprobe worked: it did.

So the question is: "Can bad weather damage ethernet cards?"

Pretty unbelievable, but I'm using old ISA ethernet NICs, probably going back to the eighties. OK, it's time to dump the old thing, but still I'm curious, anyone?

Lightning can definitely damage ethernet cards - any card can, incl. mobo.
It doesn't have to be something as strong as lightning, static electricity (from you, for instance!) could kill a computer.
If I were you I'd throw it away. It's an old computer and you don't know what more is damaged, it doesn't have to show up immediately.