[cuttysnark]

Have a look at SiteSucker[0] - an app that essentially lets you input a url and it will suck all the locally linked files/images etc. into a folder. Once you have the "guts" of the site, you can move it, grep it, edit and update it as needed. Given this appears to be a static site, you could even just open index.html in the browser (file:/// protocol) locally without having to spin up webserver while you develop.

This is the path of least resistance and perhaps the easier route versus rebuilding from scratch for a modern platform—which is also a different price tag. IMO, sucking the static site out without needing to deal with Dreamweaver on an old machine might be reason enough.

I'm not doubting the Dreamweaver claim, but I don't see any of the stink of a site generator—it looks rather simple and handwritten—doesn't even have the generator meta tag listing Dreamweaver—I wonder if Dreamweaver was only used for the FTP interface/connection to upload the files to Webhero.

My TL;DR Advice:

  1. Gain access to the old laptop only to get the FTP upload details/credentials for Webhero. 
  2. Use SiteSucker to get the whole website into a local folder on your machine.
  3. Make changes/updates by editing the files.
  4. Deploy by FTP Upload to Webhero.

[0]- https://ricks-apps.com/osx/sitesucker/index.html