Two comments: use Fcntl qw(:flock); and write flock FILE, LOCK_EX; instead of using the cryptic magic values. Also, don't unlock a locked file, ever, unless you know what you're doing - just close it and the lock will go away.

Did you check your error logs? Is the scripting dieing at the open? Btw, you should prefer the three argument form: open(FILE, ">>", "/data.txt").

If not, does your platform support flock at all? There should be something about that in your error log as well if that's the case.

Update: Also, why not use CGI.pm's perfectly fine cookie-generation functions?

print header(-cookie => cookie(
     -name    => $name,
     -expires => $expires,
     -path    => $path,
     -domain  => $server_domain,
     -value   => "there is none in your example",
));
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Makeshifts last the longest.