I would have thought that most current web site building software would enable you to manage an old site reasonably well (and so access text and images). I don't think the the basics will have changed in any material way.
If it is still a problem, you can easily copy and paste from the old website (as viewed in your browser) into the new web site software. Just highlight the text on the screen (in the browser), hit CTL+C and then switch to the web site software and locate where you want the text and hit CTL+V. You may have to do some formatting to get it to look the way you want. It may even work a bit better if you paste (CTL+V) into Notepad and then re-selectin Notepad and onwardly copy and paste from there.