I've been coding since TBL was in short pants and I have never seen this happen. I've seen bad code cause a page to barf on its shoes, but I've never seen a page that loaded and displayed according to its styling AND REFUSE TO SHOW ANY LINKS. I'm hoping this is one for the books, 'cause I sure don't want to see it again.
At my current sandbox: http://ottoprint.dreamhosters.com , the home.php page will load and display text and graphics correctly. But hover over any link (they're all over the place) and it won't do whatever it's supposed to do (mostly just change color), and the URL won't appear in the status bar. Clicking on link objects returns no results. (Well, a dumb bovine look from me, but otherwise, nothing.)
The HTML and CSS run clean through W3C's validators. This can be reproduced on (I believe) any machine and browser. It has been tested on three and in MSIE, FF, Opera, Safari, and Chrome. Flushing the cache doesn't fix anything. I've done the permalinks setting "Save changes", the .htaccess file is fine, inspected the code, read the source, it all looks fine. I've had someone who's more savvy than I look at it to no avail.
At this point, I'm hoping it's either something dumb and simple I'm overlooking or something rare and equally stupid I've never heard of, 'cause otherwise, I'm stumped.