My problem has been resolved. Blue Host helped to find the culprit.
From Blue Host:
Your issue is likely caused by the rewrites that you have established in the root of your account, I've determined this by setting up a .htaccess file in the survey directory of the account that disables the rewrites and with this in place, the surveys function once more.
I suspect that the specific culprit is your rewrite that is removing index.(php|htm|html) from URLs since the survey should be posting to a URL which ends in an index.php and the rewrite is probably destroying the data that should be getting passed on in the POST from the form.
Please let us know if we may be of further assistance.
Hope this can help anyone else who's running into the same issue. It might also be useful to have this in the documentation somewhere if it isn't already. Thanks to everyone for their help!