That's close, but you can only ever have one "object" at a time, as you're using package-level data. That means you have to access the data in the object, not in the server map. You also don't need the prototypes on methods, as they're useless here.

package myObject;

use strict;
use warnings;

use vars '$VERSION';
$VERSION = 1.00;

my %serverMap = (
    default => {
        ipaddress => "127.0.0.1",
        dsn       => "default",
        userid    => "sa",
        password  => "password",
        instance  => "instance"
    }
);

# use the arguments in $serverMap{ default } as attribute defaults
sub new
{
    my $class = shift;
    my %self  = ( %{ $serverMap{ default } }, @_ );
    bless \%self, $class;
}

sub printMe
{
    my $self = shift;
    print "------ Available Servers ------\n";
    for my $server ( keys %$self )
    {
        print "\nServer: ", $server, "\n";

        for my $cr ( keys %{ $self->{$server} } )
        {
            print "\t$cr => $self->{$server}{$cr}\n";
        }
    }
}

sub addServer
{
    my ( $self, $srvName, $hrCreds ) = @_;
    $self->{$srvName} = $hrCreds;
}

sub removeServerMap
{
    my $self = shift;
    %$self = ();
}

sub deleteServer
{
    my ( $self, $srvName ) = @_;
    delete $self->{$srvName};
}

1;
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Update: Fixed a typo in the code.