I thought I would post this because I just spent a few hours tracking this down: If you currently have a version of PHP 5 configured on your server with register_globals enabled in php.ini, PHP 5.4 will fail silently. I had PHP 5.3 with register_globals enabled (had an osCommerce install), and after I built PHP 5.4.9 through EasyApache, WHM did not detect any version of PHP, and so I couldn't activate it in the Confiure PHP screen. Running `php --version` from the command line produced no output.
Eventually I found that /home/cpeasyapache/src/error_log contained "[11-Dec-2012 01:47:54 America/Los_Angeles] PHP Fatal error: Directive 'register_globals' is no longer available in PHP in Unknown on line 0". I edited /usr/local/lib/php.ini, removed register_globals, and everything started working perfectly.
Just a heads up!