Best way to salvage a very old WP site

You will have to scrape the site for the data, or better if you have back-end access so you export the data in a file, then checking the file you can modify it to make it ready for import in the latest version, just check how it changed.

I did it before but with traditional sites that are jumping to WordPress. Scrapping the site for the data and creating either a JSON or a XML file ready for import.