It seems that most search engines don't give dead links as results, which I think is a shame. The page might not work now, but it is quite likely that the Internet Archive saved it. So the information I need probably exists, I just need to know the link in order to find it... But the search engines won't give that link since it's dead. Is there some way around this?
A dead link, see link rot, "by definition" is a "known" link that points somewhere but instead of a web page, a missing web page or website not found errors are returned.
If you don't know the link the only way to find it is to find something that holds the link you are looking for, so try think about which kind of sites could have links to that page, and search for them.