the validation show if and captcha both rely on session variables. since neither are working correctly, i would suspect the server is not properly saving sessions.
use the sessionTest page from the following thread to test the servers session management:
showpost.php?p=23826&postcount=2
If the test fails, it is most likely a problem with the session.save_path setting in the php.ini file on the server, you will need to contact the host to have that resolved.