Long running drupal site suddenly acts like it sleep()s before it renders page.

I can not figure this problem out for the life of me.... We're running 6.3

As of today, when you go to any page on the site, it pauses for about 30-60 seconds and then renders the page.

- The database has low activity
- The system has low activity
- Drupal is not waiting for mysql at all.
- Apache has a lot of connections because of all the clients that are connecting and hanging for 30-60 seconds.

The problem seems to be in the PHP.

I've tried to figure out where in the code this is happening. I think I've boiled it down to this:

In the index.php the following line:

elseif (isset($return)) {
// Print any value (including an empty string) except NULL or undefined:
-------------> print theme('page', $return); <------------------------
}

- I added a quick: print 'test'; exit; before the line above and I got my test back very quickly,
- I dug into the theme function and put my print 'test'; exit; at the last line before the function ended and I *STILL* get my test and a quick exit.
- When I add print 'test'; exit; after the above line, the application hangs as you see it now.

Other items of interest that may or may not matter:
- The accesslog table is 630M with 5,9M rows
- url_alias table has 24,575 rows
- This never happened before.

What could cause such a thing ? Has anyone ever had their drupal installation suddenly get slow like this ?