It looks like $zip isn't being created.

Try changing:

 my $zip = Archive::Zip->new();

 
my $zip;
eval { $zip=Archive::Zip->new(); } or die $@
[download]

That should provide an error message if Archive::Zip is running into problems.

Update: $! is the os_error flag. My bad. Changed to eval{} as suggested by jZed.