This question has been answered by multiple community members. See the first response.
[2012-02-12 19:36:47] (ERROR @ /fanfare/index.php) Could not cache source data for 16. [2012-02-12 19:36:48] (ERROR @ /fanfare/index.php) Could not cache source data for 16. [2012-02-12 19:44:08] (ERROR @ /Applications/MAMP/htdocs/fanfare/core/components/tinymce/lexicon/nl/default.inc.php : 12) PHP warning: include_once(/Applications/MAMP/htdocs/fanfare/core/components/tinymce/lexicon/nl/english.inc.php) [<a href='function.include-once'>function.include-once</a>]: failed to open stream: No such file or directory [2012-02-12 19:44:08] (ERROR @ /Applications/MAMP/htdocs/fanfare/core/components/tinymce/lexicon/nl/default.inc.php : 12) PHP warning: include_once() [<a href='function.include'>function.include</a>]: Failed opening '/Applications/MAMP/htdocs/fanfare/core/components/tinymce/lexicon/nl/english.inc.php' for inclusion (include_path='.:/Applications/MAMP/bin/php/php5.3.6/lib/php') /code]
[2012-02-12 19:44:08] (ERROR @ /Applications/MAMP/htdocs/fanfare/core/components/tinymce/lexicon/nl/default.inc.php : 12) PHP warning: include_once(/Applications/MAMP/htdocs/fanfare/core/components/tinymce/lexicon/nl/english.inc.php) [<a href='function.include-once'>function.include-once</a>]: failed to open stream: No such file or directory [2012-02-12 19:44:08] (ERROR @ /Applications/MAMP/htdocs/fanfare/core/components/tinymce/lexicon/nl/default.inc.php : 12) PHP warning: include_once() [<a href='function.include'>function.include</a>]: Failed opening '/Applications/MAMP/htdocs/fanfare/core/components/tinymce/lexicon/nl/english.inc.php' for inclusion (include_path='.:/Applications/MAMP/bin/php/php5.3.6/lib/php')
[2012-02-12 19:36:47] (ERROR @ /fanfare/index.php) Could not cache source data for 16.

After submitting the registration form, I get a white page.
To verify this behavior, try visiting your "Request Membership" sign-up page and submit the form without any data in it. If you get nothing but a completely empty blank white page, the cause may be due to your PHP configuration.
A simple test here is the following script:
if (function_exists('mb_ereg')) {
print 'Yes, the multibyte function exists';
}
else {
print 'No, the function does not exist. The Register Snippet may fail.';
}
The solution involves recompiling PHP. You must have the mbstring library installed and you must ensure that you have not included the --disable-mbregex option.
See this forum post for more details.