If the menu freezing problem still happened with all plugins disabled and a default theme, it could mean the culprit lies in a few other areas:
1. Browser – try this in a different browser than your usual one. Does it work?
2. Browser extensions/add-ons – try turning off all browser add-ons and extensions to see if one is conflicting. In Firefox, you can try Safe Mode:
https://support.mozilla.org/en-US/kb/disable-or-remove-add-ons
In Chrome, you can follow these instructions:
https://support.google.com/chrome/bin/answer.py?hl=en&answer=187443
Scroll down to the section called “Temporarily disable extensions.”
3. Core WordPress files – something may be corrupt in your core WordPress installation. To rule that out, you can try manually reinstalling the WordPress core files. You need to be very careful when you do that, so you don’t overwrite any important files, like your wp-config.php and .htaccess files, and your wp-content folder, among others.
The Codex has a guide to manually installing WordPress:
https://codex.www.ads-software.com/Updating_WordPress#Manual_Update
I strongly suggest backing up your entire site – both files and database – before doing a manual reinstall.