Hmm I am not sure I understand either the question or the answers! The way I read it was you wanted to comment out all lines which have the word test in them, which would look like this (also putting the close outside the loop and creating a new file rather than appending which also seems wrong!:

#!/usr/bin/perl -w
my $file_name = "test.txt";
open(INF,'./$file_name') || die "file could not open\n";
open(INFN,'>./${file_name}.new') || die "$!: ${file_name}.new\n";
my @line;
while(@line = <INF>) {
        if ( $line =~ /test/) {
            print "found at $.: $line
            $line = "\# $line";
        }
        print INFN $line;
}
close(INF);
close INFN;
[download]

If you really want to append to the file, read it in, close it and then reopen it for append. Anyway, it is usually wrong to open or close the same file inside a loop.