You can try copying the old Firefox Profile Folder to the new system, and on the new system, start the Firefox Manager > Create Profile > Next > Choose Folder > OK > Finish > Start Firefox. Even otherwise you can try to [replace/overwrite the needed files from the old profile into the new, for eg. the places.sqlite stores the bookmarks + history, key3.db and signons.sqlite are needed for the saved passwords etc.
Thanks for the suggestion. As it turned out, my salesman sold me a network cable to go with my new purchase and said it should be pretty easy to transfer existing files, etc to the new machine. When I connected it, it asked me to download a program, then transfer it by thumb drive to the old computer, then let it rip.
It worked wonderfully. Not only Firefox, but just about everything else I needed. I did have to reload the programs I use, like Office, Outlook, etc.