There is a known issue in NeatUpload about the multi file upload. Ever since an update to Flash Player several months back people have been reporting that they cannot select multiple files at once in IE and I confirm the same. A few people have reported troubles in other browsers but it has generally been working for me under FF or Chrome even though it does not work in IE for me.
Bulk upload does in fact still work but you have to choose the files one at a time, after choosing the file you click Add file again and keep going to choose all the files.
Unfortunately the original developer of NeatUpload is no longer maintaining the project. I am actually the steward of the NeatUpload project now but to be honest trying to fix this is out of my skill zone (I don't know the first thing about developing Flash and the multi file uses Flash for the file selection). It is possible that some other users/developers who use NeatUpload will step up and solve this but other than that happening I'm not sure if it will get fixed.