OK, so here are the 2 things I can tell from your post...
1) You have access to the domain, which is hosted at godaddy. All you files are on there BTW.
2) Word Press is where the site was developed and edited. You can't access these files. These files are essentially moved up to the domain through FTP.
First, I would search for the deceased login and password for Word Press. This is by far the easiest. If you strike out, try to contact WP. They may require proof that you should now own the files for this company (like you are President, Director, etc). Second, maybe reset the password using the deceased's email. You would need access to the deceased's email to do this. If you don't have it that won't work.
If that doesn't work, assuming you don't know how to, I would hire a person to download your website files from goDaddy. That way you get a local version of all the files. They can use WP or another GUI based HTML editor (Square Space, Wix, Dreamweaver, etc) to store the files locally for you, then you would link those files to your domain. The old Word Press files of the deceased would essentially become obsolete. I do suggest getting someone good to do this. It seems easy enough, but getting the files off goDaddy requires knowledge of their FTP settings, domain host names, etc. You can find them. But most developers know them already.
Good luck. Be patient. It won't happen as fast as you'll want it to.