No, it didn't find the replacements I guess.

# if called with no args param returns a list of the keys
my $w = $input->param();

# here you should validate the values for the given keys 
# and eventually set them to default values before proceeding
# $1 is just _the first succesfull match_
$page_template =~ s/\$(\w+)\$^\w/$input->param($1)/eg;
$page_template =~ s/\$(\w+)\$lc_/lc($input->param($1))/eg;
$page_template =~ s/\$(\w+)\$uc_/uc($input->param($1))/eg;
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Have a nice day
All decision is left to your taste