The easiest way to copy a site from one PC to another is to copy the actual folder where the whole site is, instead of copying the files within that folder. After you copy the folder into an external media, then you shouldn't have any problems later on when you move that folder to another PC.
Now, lets say that we still have a problem with the links. If you are linking files within a folder, where that folder is within another site, then make sure that you change the link from "/" to "/folderwhereyouhavefiles/".
Another thing I suggest is to look at the Status Bar on the browser window, and look at where the link is pointing to; that helps understand where the problem is coming from. I'm sure you know where the Status Bar is, but just in case is at the lower-left section of your browser; if you don't see it, just go View-Status Bar from your browser menu.