Sorry, forgot to mention that I used OpenDNS. I replaced the Verizon DHCP settings with those of OpenDNS. Supposedly is "safer, faster, smarter and more reliable way to navigate the Internet."

http://www.opendns.com/

Yours should work with the Verizon DNS info, or OpenDNS. Your choice.

Something else is going on
 

None of the suggestions worked. I think there must be something corrupted somewhere rather that an improper network setting. How do I uncorrupt things?

More info ---Normal ?
 

When you connect 2 computers on a LAN(at home) via a ethernet hub, router, or modem/router you should not have to do anything except enable file sharing in Network Preferences. Isn't this correct?
An apple tech checked out one computer, the G3, and said that it worked just fine on the network. I imagine the other computer would check out fine as well.

If I had an old ethernet hub or if I could just directly connect these computers via the ethernet port then I could rule out/in the my LAN Network settings.

If I remember properly, this problem started when I installed 10.4 on the Pismo in Target Mode through the G5. ??? I have 2 sets of 10.4 disks which will not install directly to the Pismo. One set is for the G5, the other is for a g4 powerbook.

I will guess that each of your Macs will test just fine on a network- by themselves. But, that's not the problem. The problem is both of your Macs do not successfully communicate to each other. Maybe the Westell does not provide good sharing capabilities between the ethernet and the wireless side - maybe some setting in the Westell.
Are you currently able to connect to the internet with _both_ Macs?
If not, then something about the Westell setup may be out of whack, and you could do a complete reset of that, double-check with Verizon for all of your manual settings.
Could also be your old wireless card in the Pismo doesn't support some part of the 10.4 networking protocols. Did the tech that checked that one try copying files while connected wirelessly? You may be able to see files, but not actually copy or move data.

response
 

I just switched from a Westell to the newest Actiontec gateway. Same problem of course. I also have the problem whether I connect wireless or wired with the G3. The sonnet airport card is only one year old.
To answer other questions: I can connect to the internet great on either computer, wireless or wired on the G3. I can copy files to either computer. Just have to use the computer that needs the new files, because I can never copy from the used computer. It's a wacko problem maybe somehow related to 10.4 and the way I installed it. Did not have this problem when the G3 was running 10.3. Not ready to go back to 10.3; not ready to purchase a retail version of 10.4 to see if this makes a difference.
I'm not sure what the apple tech did. He worked with the screen facing him, away from me. I'm sure he connected the powerbook to a new mac, not a g5. Hope he did not lie. Apple does that sometimes.
Really need someone in my home to check out every little thing.

I'm having the same problem too. When I use Finder -> Connect to Server, I got the error message in console:

Aug 6 16:14:21 MacBook automount[213]: Cannot mount URL 'smb://MSHOME;MB-VM' for /Network/Mshome/Mb-Vm (UI not allowed).
Aug 6 16:14:21 MacBook automount[213]: Attempt to mount /Network/Mshome/Mb-Vm returned 1 (Operation not permitted)

But, I can connect to the same server with Terminal smb command.
and here is my smb.conf

[global]
guest account = unknown
encrypt passwords = yes
auth methods = guest opendirectory
passdb backend = opendirectorysam guest
printer admin = @admin, @staff
server string = MacBook
unix charset = UTF-8-MAC
display charset = UTF-8-MAC
dos charset = 437
use spnego = yes
client ntlmv2 auth = no
os level = 8
defer sharing violations = no
vfs objects = darwin_acls
brlm = yes
workgroup = MSHOME
; Using the Computer Name to compute the NetBIOS name. Remove this comment to override
netbios name = MacBook

Don't exactly understand what you mean by connecting via Terminal app. I can connect, but I can't copy files FROM the host computer (Is this called the server?) only TO the host computer. Does this terminal script fix the problem?