Lost ability to change blocks and user access

On admin/build/block, changes don't register. I put a dsm() in function
block_admin_display_submit() and it's not getting there. In function
drupal_process_form there is this code:

  if (($form['#programmed']) || (!empty($_POST) && (($_POST['form_id'] == 
$form_id)))) {
    drupal_validate_form($form_id, $form);
    if ((($form['#programmed']) || $form_submitted || 
(!$form_button_counter[0] && $form_button_counter[1])) && 
!form_get_errors()) {
      $redirect = drupal_submit_form($form_id, $form);

I'm guessing that is what is supposed to be calling the submit function
that's not getting called. But it never gets to that line because the IF
test fails. $form['#programmed'] is empty and $_POST['form_id'] doesn't
exist. $_POST looks like:

Array
(
[0] => Array
(
[region] => -1
[theme] => crotheme
[weight] => -10
)
[ snip ]
[66] => Array
(
[region] => -1
[theme] => crotheme
)
)

When it's working, it looks like:

Array
(
[0] => Array
(
[region] => main_supplements
[theme] => crotheme
[weight] => -5
)

[ snip ]

[op] => Save blocks
[form_token] => 509ec7d65196c983855d5192bf29647a
[form_id] => block_admin_display
)

I have the same problem with changes not registering on admin/user/access. Other areas of the site seem fine.

Suspecting a contrib module rather than a core bug, I disabled all the contribs in the db (there's about 100 of them). That did fix it, so I started adding them back in, one project at a time like this:

* Enable module(s)
* Clear cache
* Refresh block admin page
* Move who's online block from one sidebar to the other
* Submit and see if it works

When I hit a point where it stopped working, I figured I'd found the module. But disabling that module didn't fix it. I went back and disabled the last 10 modules I had enabled and it was still broken. Repeating the whole process over fixes it again but, after a while of enabling modules, it breaks. And never on the same module.

I also notice that when I refresh the block admin page while it's working, I don't get any message. When it's not working, I get the message about the post containing data that will be resent.

Any clue? I'm stumped.

Thanks,

Michelle