It would be easier if the file content were stored in an array (or if, as suggested above, you were reading it one line at a time). Something like this -- with some of the initialization steps filled in -- could be worthwhile:

open( INPUT, "some.file" ) or die $!;

my @content;
{
    local $/;
    @content = split( /[\r\n+]/, <INPUT> );
}
my $tag1 = "whatever";
my $tag2 = "blah";

my $i = 0;
while ( $i < $#content ) { # don't test very last line
    $_ = $content[$i++];
    print "$content[$i]\n"
        if (( /35=8/ and /$tag1/ and /$tag2/ ) or
            ( /35=9/ and /$tag1/ ));
}
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I wanted to include the file open and read steps to show how to slurp it directly into an array (rather than slurping to a scalar then splitting to an array, which keeps two copies of the whole file in memory, which makes me itchy).

BTW, notice that you were using printf with a single scalar arg. Someday, if that string happened to contain "%d" or something similar, you might find the output to be different from what you intended.