You don't need a router, it's just the best thing to have. You can do it without spending any money at all. Simply buy a crossover (aka patched) cable and plug it in the two network cards. Enable TCP/IP and file/printing sharing under LAN Connection (control panel->connections) and you are done. You can share files and play games now. If you want to share the internet connection between the two you can use Windows' ICS (assuming that you have Win98SE or better) or 3rd party Connection Sharing like Wingate, Sygate, MS Proxy etc.
If you want to use Windows' ICS all you have to do is right click on the connection and select properties. Go to the last tab and enable ICS by ticking the box. You restart both machines and you are done. If that doesn't work, try assigning IPs to your PCs. The server (the PC with the internet connection) always is 192.168.0.1. The 2nd PC can be 192.168.0.2. Don't forget to put 192.168.0.1 as your Gateway on the second PC ... also use a DNS server (I'd recomment your ISP's). If you leave the DNS address blank it won't work.