Try to use the REST browser with the following URL
https://jira.atlassian.com/plugins/servlet/restbrowser

The result is a page opened with two sections,
the left one with a spinning loader in it

With a little further investigation, the problem is probably with a .js file not found and reports as 404
https://jira.atlassian.com/plugins/servlet/$webResourceManager.getStaticResourcePrefix()/download/resources/com.atlassian.labs.rest-api-browser:assets/rab/rest-api-browser.min.js

The URL includes some statement that doesn't expand to a value ("$webResourceManager.getStaticResourcePrefix()")

It's the same result in IE, Firefox and Chrome