Hey Warren,
Might the non-working site have the Secure Pages module (or something similar) running?
Sometimes the "quick/transparent switch" between HTTP and HTTPS URLs -- especially as it relates to the built-in module update process involving the authorize.php script -- can play havoc with you. If you have an HTTP/HTTPS switching configuration, try disabling it with your site in maintenance mode and see if that works.
The one mitigating factor here that doesn't jibe with my own experience is your apparent WSOD. With the HTTP/HTTPS issue, you are more likely to get your home page with a "No active batch" error message.
--Sohodojo Jim--
I'm running MAMP and VirtualHostX on my MacBook. I have a number of development sites set up that up until now have worked fine. Today when I tried to install a new theme or module after selecting the .gz file I get this URL and but then nothing happens (maybe WSOD?):
http://dev.git-test/authorize.php?batch=1&op=start&id=8
I created a fresh install of 7.15 and it all works fine. I can update modules and themes without problem.
The problem seems to be the authorize.php script. Any ideas on what I should do to make it work again?