Puzzled: any action in admin panel gets stuck on loading bar

We’ve been having real problems with the admin dashboard on our site: The page just fades out and I get a loading bar. We’ve tried in IE, Firefox and Chrome and in all of them I can’t access certain features/pages or change settings. We’ve switched off / on all but the vital plugins and are still experiencing the same issue. I have also tried updating to the latest version of WP but am now getting the same result there (page fades into loading bar but then just sits there ‘loading’ forever).

Our site is a custom theme but has worked fine until now. It’s running on WP 3.6.1 so not really that old.

Has anyone had anything like this before and any suggestions for how to resolve this?

Thanks in advance for any help…