You're not quite there with filehandles, yet. First you are telling Perl to get each line (actually record) in a file, one at a time, using while. Then you're making a reference to that same filehandle again while the line you want is already in the special variable $_.

Try this (untested) code:

print header, start_html('log parsing');

open(FILE, "<", 'log.txt') or die "Cannot open file: $!";

while (<FILE>) { #  $_ is your message, but you could also
                 #  say "while my $message ..." to store
                 #  each line in $message  
  
  chomp;  # gets rid of newlines, etc.
  
  if ( m/(^Alberta226:)\s+(.*)/ ) { #  you just need 
                                    #  the one anchor

    print "$1: $2<br>\n"; # add a newline for HTML output legibility
  }

}

close (FILE) or die "Cannot close file: $!";
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