$content =~ s#.*<h1>Random Movie Quote</h1>(.*)<P><form method=get act
+ion="/Games/randomquote.html">.*#$1#s;
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However, for extracting a string from some text, you are better off matching and just using the extracted string, rather then trying to substitute out everything else in one step:

if ($content =~ m#<h1>Random Movie Quote</h1>(.*)<P><form method=get a
+ction="/Games/randomquote.html>#s)
  $content = $1; # we matched, replace $content with $1.
                 # though it might be clearer to put it
                 # in a different variable.
} else {
  # we didn't match, complain.
}
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(Note that similarly you can check the return value of s/// to see if a substitution actually took place.)