#print $hash{key} "This is line 4.\n";

Note {} curly braces around $hash{key}:
    print {$hash{key}} "This is line 4.\n";

Update: From print:

If you're storing handles in an array or hash, or in general whenever you're using any expression more complex than a bareword handle or a plain, unsubscripted scalar variable to retrieve it, you will have to use a block returning the filehandle value instead, in which case the LIST may not be omitted:

    print { $files[$i] } "stuff\n";
    print { $OK ? *STDOUT : *STDERR } "stuff\n";

(Update: The documentation excerpted here refers to Indirect Object syntax. Please see kcott's ++reply and the replies of others in this thread for the way to avoid this syntax and for the wisdom of doing so.)