If I understand correctly, you're switching to a new box/OS. This means you may need to check your web server settings, the permission settings of the directory you're trying to upload to, the user id that the script is running as, etc. There are many things that could cause problems - none of which have anything to do with the perl code used in the upload script!
Comment on Re: Getting a filehandle for uploaded file
Thanks to everybody here. Steve's comment made me go and check the form tag, which had method="action".
I had achieved that by passing CGI::start_multipart_form some wrong parameters. I was passing a hash (method => 'POST', action => 'action.pl'). It actually takes a list ('POST', 'action.pl').