I mentioned in my reply to ZZamboni that I was testing a program in which I was reading data from a config file. I created the string with text to simulate what I was reading from the file.

I decided a different approach:
I created a text file with the line $$NETOBJ.parameter in it. Then I changed my code to the following:

#!/usr/local/bin/perl

open (F, "textfile") or die "Could not open file: $!";

$a = <F>;

$a =~ s/\$\$NETOBJ\.//;

print $a;
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This code outputs parameter. It turns out that the way I was simulating reading text from a file was part of my problem.
Thanks to everyone for the help.

Humbly,
Tii