If you are referring 兩部電腦 as two desktops, router is NOT a must thing to share internet connection. You can share internet connection without having router and you can also share files between the 2 PCs. Here is how:
http://hk.knowledge.yahoo.com/question/?qid=7007091102412
Depending on how you want to share your internet connection..... If it is only for basic internet surfing, checking emails & stuffs, no need to buy router, just follow what I suggested which means an extra LAN card will do the trick instead of paying 300-500 for a router.
If you play online game a lot, router is the solution as it will do IP address routing for you (Router will assign different IP addresses for each device connected to your network so that it will not share the same IP; some online games will not allow the same IP to play online games).
Since you mentioned Not connecting wirelessly, I assume your 2nd PC is not a notebook or laptop; otherwise, you could have wireless router for internet connection in bathroom or any other rooms.
HTH
2007-10-16 01:19:40 補充:
refer to the following answer for how to install router
http://hk.knowledge.yahoo.com/question/?qid=7007100404924