Okay, I had attempted to be explicit. Let me try again.
Plugin conflicts: As I said above, I manually reset all my plugins without an impact. Just to be clear: I did exactly what those instructions called for. (In fact, the codex page isn't complete; it doesn't mention mu-plugins.)
Theme conflicts: Sorry, I failed to mention this. Yes, disabling all custom themes results in the same issue.
.htaccess: I'm running nginx, not Apache, so that of course means this advice isn't relevant. That said, without changing nginx's directives, this was working on 3.0.3. Unless you know of some change in 3.0.4 that would cause a need for changed rewrites?
Detailed error message: here's the complete error message I'm currently getting if I call wp-admin.
^X2011/01/02 11:40:40 [error] 8627#0: *21240 FastCGI sent in stderr: "PHP Fatal error: Call to undefined function set_screen_options() in /home/noisepages/www/wp-admin/admin.php on line 66" while reading response header from upstream, client: 220.127.116.11, server: noisepages.com, request: "GET /wp-admin/ HTTP/1.1", upstream: "fastcgi://unix:/dev/shm/php-fastcgi.sock:", host: "noisepages.com"
Note that that error message remains even with all themes and plugins disabled.
What would cause WP to fail to load core functions?
I'll continue to investigate; thanks for your help.