The error simply says, Magento couldn't find Zend_Log class inside your application. By default, this class resides in \lib\Zend\Log.php1. So the first thing that you want to make sure is, this class exist in your magento instance.
But the bigger mistake that I can see here is, there is a Core Hack, which you should never do in Magento. If you want to extend Magento functionality, you should either do a rewrite or if possible, use an event handler.
In this case, default Mage_Checkout_Block_Onepage class do not have a method getAddressesHtmlSelect(), but it's parent class (Mage_Checkout_Block_Onepage_Abstract) has one. So I doubt someone is trying to modify it's parent class method behaviour by directly putting the method inside Mage_Checkout_Block_Onepage. This is completely wrong.
I am enforcing the point. "In order to do this, you should either use any event handler or rewrite the class Mage_Checkout_Block_Onepage".
Note : We can't see any Zend_Log class usage in the provided code. So further help is not possible, if you didn't provide more details.
1 - Zend Log class
Best Answer
If you use anything like APC / Redis of other sorts of cache be sure to really empty it correctly. this is most of the times the issue on this kinds of errors. You can empty it by download the apc.php you can download it from the packages here http://pecl.php.net/package/APC
Let me know if thats solves it.