Second ethernet card seems to cause networking failure?

[Frank Miles <fpm@u.washington.edu>]

I recently added a second networking card to a hardware-test PC.  This elderly machine
had been working reasonably well.  The second networking card is for eth1, etc., and
/sbin/ifconfig shows things as properly connected, with eth0 being the outside interface
and eth1 being an internal 192.168.x.x interface for some special internal systems that
have absolutely no need to communicate with the outside world, just this one PC.

The weird thing is that with normal booting configuration, pinging INet addresses
fails.  This seems to be related to the order in which the interfaces come up: doing
	ifdown eth1 ; ifdown eth1 ; ifup eth0; ifup eth1
causes pings to fail; but if eth0/eth1 are reversed (bringing up eth0 last), or eth1
is simply suppressed, pinging URLs works (i.e. ping www.debian.org).

Regrettably this last does not entirely solve things - for example, I cannot do system
updates: "apt-get update" fails to connect.

Eventually, if I play around long enough (killing eth1, killing my firewall - which
hasn't changed since before adding the second NIC,...) I can do a system update
but it's not entirely clear what the critical steps were to get that working.

I freely admit that I'm a hardware guy - I don't know much about networking.
Does anyone have a suggestion on where I might look to get this working properly?
Without sacrificing eth1?  Or at least some better diagnostic[s] to track down
where packets are getting lost?

TIA!
	-f