Changed my CPU & Lost Internet Connection

I have a Cox Motorola Moderm and Linksys Router.

I have a set up of 1 Desktop and one laptop which uses wireless connection.

Any time I try changing my CPU (CPU_1) for the desktop to another one (CPU_2) I loose my internet connection. When I reconnect CPU_1 to the set-up I get the internet connection back.

I really need to change CPU_1. Can I get help please.

Thanks.