well it all depends on which dialup service you conenct to. if you connect to verizon quick2net or expressnet, you need to use their smtp server. if you dial up to another isp like earthlink, aol, or juno, or smoething, you obviously need to use your regular smtp server.

try to telnet to the smtp server on port 25 and see if you can connect. if i understand correctly, you cant even connect if you are within the verizon network.

which mail client are you using on the pc? double check that it is in fact setup properly to provide hte user/pass to the smtp server (in outlook its "my outgoing server (smtp) requires authentication")
it also might be referred to as ESMTP