With a network adapter in both PC and laptop, they can be connected with a crossover CAT5 ethernet cable. By setting up Internet Connection Sharing in the PC with the broadband connection, the laptop can connect while the PC is running.
To be able to connect independently without having to rely on a 'host' PC being connected, you would need to use a router. As routers connect by ethernet to both the PCs and the modem, a USB modem cannot be used. You would therefore either have to replace the USB modem with one which connects by ethernet cable or buy a router with built-in ADSL modem.