Don’t be fooled: the SerialConnect application has nothing whatsoever to do with PPP or establishing Internet connections — it’s just for dialing into BBSes, programming your modem or terminal adapter, or for trapping kernel debug information.
To make an Internet connection, just establish your TCP/IP settings in the Dial-Up Networking panel and start a service — check your mail, click a link, or start an FTP session… your default PPP connection will be initiated automatically. Note that dial-on-demand services were absent in the R4.0 release, but are restored in R4.1 and later; in R4.0, you’ll need to establish PPP connections via DUN’s Deskbar replicant or from the DUN application itself.