The way you have it written, there's an extra newline before the From: line, which will probably cause problems (you don't want a blank line in your headers). Have you tried:
open(MAIL, "|/usr/lib/sendmail -oi -t") || die "Can't open sendmail: $
+!";
print MAIL qq|From: Me <me\@here.com>
To: You <you\@there.com>
Subject: Email
body text|;
close(MAIL);