The ability to upload multiple files simultaneously is provided by flash upload. This kind of upload is possible in case browser is allowed to use flash player.
Please check if your Chrome and Firefox have flash player disabled. In the request the cookie which contains the version of flash is sc_fv.
Enable flash player in Chrome - Enable Flash in chrome
Enable flash player in FireFox - Enable Flash in Firefox
*please let me know if u have any questions on this and i can come back as soon as possible