While it's never clear if a person can or can not accomplish such things, the web site http://www.wown.com documents such a setup.
Be aware that your stock Zone Alarm will kill off the LAN and that trips up too many. Install the needed patches, eject Zone Alarm until it works and then install your firewall.
Since all the setup information is there, I won't copy it in here. Many find the setup too hard to setup. In fact, harder than getting the router.
I have a Dell Dimension 4600 running french WinXP home edition and a notebook running chinese Winxp pro, both are equiped with a ethernet card. Can I connect the two machines together with a coaxial cable without a router and having the printer and internet connection shared.