Serial cable is stone age stuff.
Best to connect the PCs directly together with a physical network cable (might need to use a cross-over), or connected to the same router (wired or wireless), or remove the hard disk from the old PC and connect it as a second hard disk to the new PC (internally or externally).
Lots of helpful guides available on migrating user data from one system to another - Windows ships with a Wizard to do (some of) it, but you have to run it once for each account you want to migrate.
You basically want to copy settings and data from C:\Documents and Settings\username to the same location (or a backup location) on the new PC.
SD