How to troubleshoot WLAN WPA2/WPA not working after updating to OSX 10.8.4?
Since the update told you it failed, you might need to re-apply the update by connecting to a wired network or downloading the whole update from another computer if yours is off the network.

Be sure to download the 10.8.4 Combo updater and re-apply the update to be sure the drivers all installed properly and no pieces of your software were missing or corrupted. Since normal updates are a delta (only the changed items get written), it's a slim chance that something odd happened and a re-install of the patch might help fix things up for you.

Once you've gotten the OS X update installed, should the problem persist, you can troubleshoot it as normal. The two avenues I would pursue to troubleshoot this would be to dig into Wireless Diagnostic first to see if it can identify your issue.


/System/Library/CoreServices/Wireless Diagnostics.app


This tool is substantially better on 10.8.4 than it was on previous versions (when it was called Wi-Fi Diagnostics) and it has helped me solve several tricky network issues already.

The second would be to go into the Network preference pane and clear all known wireless network settings:


Network Preference Pane
Wireless
Advanced
Delete all preferred networks
Then make a new "test" location and try re-joining the affected network (or joining another network to ensure this isn't just a coincident failure of the wireless card and not related to the update)