You have two options and neither involve using the modem.
If you have a switch or Broadband router that both computers CAT5 cables can plug into then you can use that and play with the LAN mode.
If you don't have a switch/router then your next bet is a crossover cable.. if you have stuff there you can make one or you will need to purchase one..
http://www.littlewhitedog.com/content-8.htmlIf you use the crossover cable then you need to set your TCP/IP settings manually.. make one computer 192.168.50.10 (255.255.255.0) and the other 192.168.50.20 (255.255.255.0) and then your computers can talk to each other.
Don't know where you live but you can call a local computer repair place and they could probably make/sell you a cable for 10-15 bucks..