The first thing you need to do is go out and get yourself a copy of the Lama ("Learning Perl") and read it, or read through some of the Perl documentation such as perlintro. You will also find a pile of good stuff in the Tutorials section.

Next, always start your scripts with strictures:

use strict;
use warnings;
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That will help pick up silly errors and typos. Often the errors won't make sense initially so you could throw use diagnostics; into the mix as well, or ask here. Your given code would be better written:

use strict;
use warnings;
use diagnostics;

my $logName = 'logfile.txt';

open my $logIn, '<', $logName or die "Can't open $logName: $!\n";

while (defined (my $line = <$logIn>)) {
    ...;
}
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which uses strictures, the safer three parameter version of open, safer and better behaved lexical file handles, better failure diagnostics and a while loop instead of slurping the file.