First, please make sure that your browser is up to date by visiting http://whatbrowser.org/
If it is not, please try updating your browser or switching to a different browser.
If it is, please do these two things:
1. Try clearing your browser’s cache and cookies.
2. Try with all browser extensions or add-ons temporarily disabled.
Please let us know how each step goes for you, and which browser (and version of) you’re using if you’re still having trouble.
I am using two different browsers: Chrome 44 and Firefox 39 (both current.) I have cleared cache and cookies in both – no effect. Turning extensions on and off in both also has no effect.
The current version of Firefox is 40.0.2. Would you please try that?
Done. No effect. Also, I have other WordPress sites running the same version and on the same browsers. They work perfectly. I can upload/add images in the media library just fine, but the Customizer does nothing and I need it to change out logo, headers, etc.
Update: I went back and installed WP 4.1 and now it works just fine. I have no idea why it didn’t work after the last two versions came out, so I guess I just won’t be updating again for a while.
Well, the next thing I was going to ask if it worked fine in a different theme, like Twenty Fifteen. It’s possible that the developer of your theme just hasn’t updated to the new customizer.
It’s fine to stay on 4.1, you’ll just be missing a few security fixes for publicly known vulnerabilities.