I finally got it using this:
{{block type ="Mage_Customer_Block_Form_login" template="customer/form/login.phtml" }}
Instead of pulling in my own custom block. Not really sure what the difference was until I looked at the source code and noticed there was a slight difference in the action attribute.
mageUz'smageUz's answer was very close. So instead of this:
<?=Mage::getUrl('customer/account/login', array('_secure' => true))?>
it was:
<?=Mage::getUrl('customer/account/loginPost', array('_secure' => true))?>
All it needed was Post added to it. Then I removed the Mage block and just kept mine in there.
Thank you guys for the help and putting me in the right direction.