First there was a message about my upload size being to small. I then set all the PHP.INI parameters and they are reflected in phpinfo().
No more error message, but with every upload (in the download section of the product) it just stalls at "Uploading..." whenever I try something larger than 20MB.
Thanks for trying to help, but, yes, I checked those and it is not a PHP problem. It seems to be a problem of that Javascript uploader.