I’m having a similar problem and it appears to have something to do with wp-cache-base.php in the supercache directory. I’ve been adding echos to various parts of the code to see how far everything executes, and nothing seems to happen after this line in wp-cache-phase1.php:
include( WPCACHEHOME . 'wp-cache-base.php');
wp-cache-base.php just declares a $known_headers array and the CacheMeta class if it doesn’t already exist. That’s it. Putting echos in this file seemed to fix the blank page problem for a while (!!!) so it’s hard to tell how this file is affecting things, if at all. Strange. Once a page was loaded properly after adding an echo, the file could be set back exactly as it was and everything worked fine. Again, for a while. I’m waiting for this to happen again.