Have reviewed your install further and it's because you are conditioning the same field like 5 times. That is not going to work. Condition it once properly. There is also no reason to set a field as non-required if it's set to be hidden as it'll already handle the required state swapping.
For example "Company Name" conditions it self based off "Employment Status". So "Employment Status" does not need to condition "Company Name" or you end up with multiple conditioning. You can see this by editing "Company Name" and below the conditionals it'll tell you want field is conditioning it. You can confirm this by disabling all the conditionals in "Employment Status" and it'll work fine.
Warning: is_readable() [function.is-readable]: open_basedir restriction in effect. File(/dev/urandom) is not within the allowed path(s): (/home2/networke:/usr/lib/php:/usr/bin:/usr/php4/lib/php:/usr/local/lib/php:/usr/local/php4/lib/php:/tmp) in /home2/networke/public_html/libraries/phpass/PasswordHash.php on line 51
That's coming from Joomla and is just a warning so that's not going to stop registration. Post this error to the Joomla forums or contact your host regarding it.
krileon
