I agree with grantm, you should always use absolute paths in scripts that need to run as a cron job. From what I gather (man crontab), the script is probably invoked from your home directory. A workaround might be to use FindBin to locate the directory the script is in.

In addition: your code isn't very Perlish. I'll try to Perlify it a bit, mainly by using grep(). Plus, you're only looking for files, not directories, are you? The test can be simplified, that way.

#!/usr/bin/perl -w
use FindBin;
chdir("$FindBin::Bin/..");
opendir(DIR, '.');
@dir = readdir(DIR);
closedir(DIR);

if(my @new = grep {-f and $_ ne "index.html"} @dir) {
    # send mail...
    # ...
    print "New files:\n";
    print " * $_\n" foreach @new;
}
[download]

I used chdir() because otherwise the filetest won't work.