patch 9767 adds form keys to the following forms:
Shipping cart form:
app/design/frontend/<package>/<theme>/template/checkout/cart/shipping.phtml
Multishipping billing checkout form:
app/design/frontend/<package>/<theme>/template/checkout/multishipping/billing.phtml
Multishipping shipping checkout form:
app/design/frontend/<package>/<theme>/template/checkout/multishipping/shipping.phtml
Billing checkout form:
app/design/frontend/<package>/<theme>/template/checkout/onepage/billing.phtml
Shipping checkout form:
app/design/frontend/<package>/<theme>/template/checkout/onepage/shipping.phtml
Payment checkout form:
app/design/frontend/<package>/<theme>/template/checkout/onepage/payment.phtml
Shipping method checkout form:
app/design/frontend/<package>/<theme>/template/checkout/onepage/shipping_method.phtml
Persistent Billing checkout form:
app/design/frontend/<package>/<theme>/template/persistent/checkout/onepage/billing.phtml
What to do:
If you're using with custom versions of those templates you'll have to update them by adding the following code into them:
<?php echo $this->getBlockHtml('formkey') ?>
For more reference,
https://magento.stackexchange.com/a/176958