I found out that disabling Flashblock plugin for Chrome shows the upload 'window'.
However, it now gives another upload error message (when using jquery) Error: SyntaxError: Unexpected token <
(screenshot of error messages http://i.imgur.com/wCIfdg3.png)
When using http method, the error Fatal error: Invalid album instantiation: . does not exist. in ...\zenphoto\zp-core\class-album.php on line 726 comes up.
I've checked that I have the required plugins in zp-extensions, and have also reuploaded them.
Any ideas what's wrong?