Your issue may have something to with used_in_forms keys didn't get deleted.
Mage::getSingleton('eav/config')
->getAttribute('customer', 'demande')
->setData('used_in_forms', array('adminhtml_customer', 'customer_account_create', 'customer_account_edit', 'checkout_register'))
->save();
Take a look at database table customer_form_attribute
and compare it with a older backup
To remove attribute the correct way
/* @var $installer Mage_Eav_Model_Entity_Setup */
$installer->startSetup();\
// Remove Product Attribute
$installer->removeAttribute('customer', 'product_attribute_code');
To fix your issue see Call to a member function getBackend() on a non-objectCall to a member function getBackend() on a non-object