Trapped! the login info to an old site of mine died with a friend.

Background: Long story short, my friend built a website for my business a long time ago and then passed away in 2012. With him, he took the login info to a site built in 2008. It is so very outdated and broken, but it comes up first for all my clients when they search for my business. I'm guessing because of its longevity?

I still have the login info to the domain hosting website so I can reroute the domain to a new site. (I'm planning on just making a Squarespace site so I don't have to deal with HTML ever again)

Question: If I reroute my domain to a new site will my SEO score (not sure what to call this) go down? Is SEO attached to the domain name or the website that it points to?

Thanks for your help in advance!