The PowerBook Memory Source page is reporting that both the modem offer and the Apple-Citibank Credit Card rebate offer require that you send them the lone original UPC symbol for the PowerBook. (Thanks Bryan Goldstein).
Ricardo Davis writes that the modem offer is for a choice of a 33.6 PC card modem from either Dayna or Megahertz. However, Ricardo claims that Megahertz has confirmed that their modem does not currently work with the 1400. They expect to release a fix "in a month or two."
Update: The MegaHertz CruiseCard modem is the one included with Apple's free modem offer. This one does appear to work with the 1400 (according to reports I have now received). It seems that it is the Megahertz Ethernet*Modem 33.6 PC Card that does not work with the 3400.