You should never update Wordpress without checking if all your plugins and theme are compatible with the newest version. This is always important to remember with wordpress and even more so when going up an actual version number (3.4.x to 3.5 and later 3.6).
A couple of things, your Corona theme files are out of date and should be updated to the most recent release of 1.4. Version 1.3 was the update to make the theme compatible with Wordpress 3.4+ and 1.4 has a big security update for the framework.
Look into that and make sure to download the most recent version of the theme from Themeforest from your Downloads. You can update just like you first installed the theme and if you've made any changes to the theme files themselves, you'll have to re-add in those changes. You can also update only those files that have been changed in the theme by looking at the version.rtf that comes in the main package you download from theme forest.