# initialize the array of patterns
# the same code as you use in your script, just complete the line
my @pat_array = ...;

# this is new hash variable used for counting matches
# it used entirely instead your approach
my %match_count;

# skip first lines
# simple read them and do nothing over them
<LOG_READ> for ( 1..$InStartLineNumber );

# normal work
# read line by line the rest of the file and do something
while ( <LOG_READ> ) {

	# read the line, and store in the variable explicitly
	chomp;
	my $line = $_;

	# walk through the list of patterns
	# test the line for matching each pattern
	# and count every successful match in the hash
	map { $line =~ m/\Q$_\E/ and $match_count{$_}++; } @pat_array;

}

# The rest of code handling with @pat_array and %match_count