Sure sounds to me like a bad Miami config. And, note that just because your modem is online and connected doesn't necessarily mean your TCP/IP stack is.
I believe that you are wrong. We are talking about a dial-up modem not a DSL router. Dial-up modems doesn't auto-negotiate/connect. They let the stack do it. Unless he has a special kind of modem that i'm not aware of..
@Daniele
Anyhow, i also believe that you have misconfigure MiamiDX.
Use miami, not MiamiDX for dial-up. It's more light and easy to configure.
Are you sure that you have set serial.device unit 0, and not another one?