I'm having this problem too (UBB6 beta 7.1) -- I tried Phoenix's solution, but no dice. I've done two installations -- one as an upgrade, and one as a new installation. In both cases, attempts to create a new registration give me the blank screen (for the new installation, that means I can't create the original administrator profile).
ubb6_test.cgi confirms that my directories and permissions all check out. Modules is at 777. I don't have access to my perl installation to see if my perl module permissions are out of whack as cdnArmy suggests above.
At the moment, I'm dead in the water, but it looks like I'm in good company with this bug, looking at other posts across the board.
Josh