Admin Post and Plugin Search kicks to blog home page – Spooky Mystery

Ok, this mystery needs to be solved. For more than 2 years, the search box in the admin section has kicked to the front page instead of search results. This is true for searching posts, searching pages, and now searching for plugins as well. This is the only install I’ve seen this on (of over 100 I’ve worked with) and I kind of think it’s a problem somewhere deep in the database, since I have re-installed, changed templates, checked plugins.
Anyone ever seen this before?