$constant = quotemeta '$$';
$line_count =0;
while (<FILE>){
  if($constant ne "") {
     if($_ =~ m/^($constant)/) {
       $line_count++;
     }
  }
}
[download]

UPDATE: Geez... you asked this question 2 days ago, and got the answer --

G'day sowais,

That's exactly the same question, title and text, that you posted yesterday: "Issue with regex matching".

Furthermore, you appear to have updated yesterday's post with:

"Thank you all for your input! I have my code working using quotemeta."

Clearly, there's something wrong here; although, I don't know if you've pasted the wrong question from wherever you do your editing, somehow reposted in error, or something else. "How do I change/delete my post?" should be able to help you decide how to fix this.