Or just store the original key as the value of the canonicalized (lower-cased) hash. Look up in the lower case hash to find the key, then use the value of that hash to look up the value in the original hash.

#! /usr/bin/perl

%hash1 = ("John", 43, "Paul", 25, "Marie", 22);
%hash2 = ("john", 43, "Paul", 25, "marie", 22); 

my %lc_hash1 = map { lc $_ => $_ } keys %hash1;

while (($KEY_2, $VALUE_2) = each %hash2){
    if (exists $lc_hash1{lc $KEY_2}){
         print "$KEY_2 : Matched\n";
         print "Keys are: $lc_hash1{lc $KEY_2}, $KEY_2\n";
         print "Values are: $hash1{$lc_hash1{lc $KEY_2}}, $VALUE_2\n";
    }
    else{
         print "$KEY_2 : Did not match\n";
    }
}
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