You don't see any problems here?

$i = 0;
my $filename2 = "invaildAddress";
$arrayLength = scalar(@addressSave);

print $arrayLength ."\n";


open(IN2 , '>', $filename2);
print IN "Invalid Addresses:\n\n\n";
while($i > $addressL){
    
##########BROKE?
  
    print IN2 "City = " . $invalidAdd[$i]->{City} . "\n";  
    print IN2 "State = " . $invalidAdd[$i]->{State} . "\n";
    print IN2 "Zip = " . $invalidAdd[$i]->{Zip} . "\n";
    print IN2 "Address = " . $invalidAdd[$i]->{Address} . "\n";
    print IN2 "Po Box = " . $invalidAdd[$i]->{PoBox} . "\n";
    print IN2 "Suite = " . $invalidAdd[$i]->{Suite} . "\n";
    print IN2 "Misc data = " . $invalidAdd[$i]->{MiscData} . "\n\n";
    
$i++;
}

close(IN2);
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First you set $i to 0. Then you open a file with the handle "IN2" for output, but fail to check open for success. Then you print a line to the closed filehandle named "IN". Then you have a while loop that never executes because $i still holds zero, which should never be greater than $addressL. Since the only lines that print to IN2 are inside of a loop that never executes, you get no output. Within your loop at least you're trying to print to the correct filehandle.