that links have been changed "by the software", what software do you mean? You're not using any software if you edit HTML code in Notepad.
A web browser looks at the HTML and displays it as a web page, it doesn't alter anything in the server dorectories - it can't.
The reason the site didn't work on another computer is because you were referencing files that are on your hard drive - and they aren't on the other machine. If you want to test the site properly you must make an FTP transfer of your revised HTML pages (plus any image or other files that are referenced) to directories on the site's host server. Be aware that doing this will overwrite existing pages with the same filename.htm, so it would be sensible to back the server copy up (to your hard drive) first.