There is no file named "upload.php", there are "uploader.php" ones within "zp-core/admin-httpupload" and "zp-core/admin-upload.php". MAke sure you really installed everything correctly.
You have the choice between a flash multifile upload, the normal form upload and even directly via FTP.
Because the installation routine is fully automatic the error quote is quite low I guess. I took 2 screenshots, see for yourself.
//the upload-Button I was talking about
http://i56.tinypic.com/34zkpiq.gif
//thats what I got after "clicking" on upload
http://i51.tinypic.com/1zqr41c.gif
Besides that, the green "hochladen" bzw. "upload"-button shows no reaction at all.