Hi Michelle,
We're all sorry for your loss. Your dad was a cherished member of our community here.
If you or your brother are interested in bringing his website back online permanently, I could help with the technical side of things, and host it for free on this site indefinitely.
It looks like the troutnut.com/libstudio domain name has lapsed (and would cost some money to annually renew), so it would probably be difficult to bring the pages back at their original address. However, I could put them online at addresses like http://www.troutnut.com/libstudio/original-filename-here.html. I would keep the pages as they were, except for a brief explanation of why they're hosted on this domain name (and probably a link to these forum threads).
To do this, I would need the actual files from his website (both the images and the webpages). There are two potential ways to get them, and I don't know which one (if any) will work, because it depends on the technology he used.
Method 1: The files might all be on his computer. By looking at links to his site that he posted on here, I can give you some keywords to search for (unique names of some of his site pages): tup_s_indispensible.html, li_l_dorothy.html, sulfur_soft-hackle.htm, StomFlu.jpg, TupsWoolinLight.jpg. If the site files are all on his computer, running a search for any one of those should find the whole thing.
Method 2: The files might still be on his former hosting company's servers, even if his hosting account expired. If you have access to his email, you might be able to search it (possible search keywords: hosting, libstudio, troutnut.com/libstudio) and find out (a) who his hosting company was, and (b) his login/password with them. If you could share those with me, I could log in, briefly reopen the account if they still have it on record, and find and transfer the files. If you're not comfortable doing that, you could have someone you trust retrieve the files from there.
Feel free to private message me through this site or email me at jason@troutnut.com if you'd like to give any of this a try.
Jason Neuswanger, Ph.D.
Troutnut and salmonid ecologist