Router question

I have 2 computers. I use one for work and the other for everything else. They are side by side. I use 1 monitor for both computers, so of course it would be impossible for someone to use my personal computer while I am working.

I have been researching routers, but I really have no need for one, do I? All I have to do is connect the DSL to the work computer when I work, and take it out and connect it to my personal computer when I use it right? So the router wouldn't be necessary, right?

Follow Ups:

• There IS a switch - I have one. - Holli 09:55:13 09/14/04 (0)
• There is some type of switch - Shellie 15:18:06 09/13/04 (0)