Image 'select files' button not doing anything (I've tried many fixes)

When I try and add images to a post (or to the library) neither the ‘select files’ or the ‘browser upload’ do anything, by which I mean they literally do nothing, no time out, no errors, just nothing. In fact the button shows top left of the dialog box instead of dead centre like it usually does.

This is a new install https://www.rollhandling.co.uk – it is installed in a 1and1 hosting package that has all my other (totally fine and healthy) wordpress installations (not multi-site).

Here’s what I’ve tried so far (rolling back to default after each failed fix attempt):
Clearing my browser cache (and restarting)
Trying the button in FireFox, Chrome and IE
Increasing memory limit in a php.ini file in wp-admin
Increasing memory limit in .htaccess
Increasing memory limit in wp-config
Disabling each plugin in turn
Disabling all plugins by renaming the plugins folder
Replacing the root files on the sever, wp-includes and wp-admin with the files I originally downloaded
Replacing the root files on the server, wp-includes and wp-admin with files downloaded from www.ads-software.com
Checking that there is an uploads folder in place
Trying the button / link on another computer
Disabling mod_security using a .htaccess file in wp-admin

I’m running out of ideas ??