# The three-argument version of open, and using lexical variables is preferred
open my $LOG_READ, '<', $InLogFilePath or die "Can't open file $InLogFilePath: $!";

# Read the next line into $current_line
while (my $current_line = <$LOG_READ>) {

    # Ignore the first $InStartLineNumber lines of the file
    next if $. < $InStartLineNumber;

    # Process current line
    . . .
}
close $LOG_READ;