Thanks for your feedback, Gabe and Florin.  Unfortunately the fix I posted 
about earlier is no longer working, for reasons I don't understand, so .  
Here's the info you requested:

On Wednesday 02 January 2002 11:05, Gabe wrote:
> You prolly don't have a route.  When you run 'netstat -rn', do you see a
> default route?
And Florin likewise wrote:
>Try rebooting the problem machine and run /sbin/route -n and post the result 
>back.

After a reboot, here's what I get from both commands:

Kernel IP routing table
Destination     Gateway         Genmask         Flags   MSS Window  irtt Iface
192.168.0.0     192.168.0.1     255.255.255.0   UG        0 0          0 eth0
192.168.0.0     0.0.0.0         255.255.255.0   U         0 0          0 eth0
127.0.0.0       0.0.0.0         255.0.0.0       U         0 0          0 lo
0.0.0.0         192.168.0.1     0.0.0.0         UG        0 0          0 eth0

I take this to mean that eth0 is the default route.  (How can I get rid of 
that first entry?)

When I connect with PPP, the table changes to this:
Kernel IP routing table
Destination     Gateway         Genmask         Flags   MSS Window  irtt Iface
216.160.33.1    0.0.0.0         255.255.255.255 UH        0 0          0 ppp0
192.168.0.0     192.168.0.1     255.255.255.0   UG        0 0          0 eth0
192.168.0.0     0.0.0.0         255.255.255.0   U         0 0          0 eth0
127.0.0.0       0.0.0.0         255.0.0.0       U         0 0          0 lo
0.0.0.0         216.160.33.1    0.0.0.0         UG        0 0          0 ppp0

Florin continued,
>What's in your /etc/resolf.conf immediately after reset and after dialing
>out?

Assuming you mean /etc/resolv.conf, it lists the domain name of the ISP I no 
longer use ("search tcfreeisp.net") and then a dozen or so nameservers I've 
collected, and then "options rotate timeout:15".  Should I manually edit this 
file to search my new ISP's domain?  Should there be something else in this 
file that's not there?  Does resolv.conf even come into play when I'm typing 
in IP numbers instead of domain names?

When I'm using PPP, resolv.conf has an additional (temp) search entry with my 
actual ISP's domain name, plus five more nameservers.

Florin proceeded to ask incredulously,
>Are you telling this box that the default gateway
>it's itself? That's wrong. The default gateway is used to send the packets to
>networks this computer doesn't know about.

No, 192.168.0.1 is the other box, which I hope to use as a gateway once I can 
reach it reliably.  The box with the problems is .42 or .43, depending on 
which I last changed it to in my tinkering.

Florin recommends:
>You should try to remove that line from the configs in /etc/network....

I have no /etc/network, so my configs must be elsewhere.  What am I looking 
for?

Thanks again!  --Ben