I'll put all of my money in my pocket on a guess that you're using Firefox 5.0? (Note: All of my money in my pocket equates to about $0.75, so don't get too excited).
The dining reservations application has been having issues with Firefox 5 since it was released a few weeks ago. For now, switch over to Chrome or MSIE (ugh) and it should work for you. If it still doesn't, then there's something else going on. Try clearing the cache and if all else fails, pick up the phone and talk to a person (I know I know, I absolutely hate it too... )