Win32API::File seems to provide the required low-level calls. So, I played around a bit, essentially reverse engineering some C code I found here, and something like this does work for me (tested on Win XP):

use Win32API::File qw(CreateFile DeviceIoControl :FILE_SHARE_ :Misc);
use Win32::TieRegistry;

sub IOCTL_NDIS_QUERY_GLOBAL_STATS () { 0x17 << 16 | 2 };
sub OID_802_3_PERMANENT_ADDRESS   () { 0x01010101 };
sub OID_802_3_CURRENT_ADDRESS     () { 0x01010102 };

sub NDIS_Query {
    my ($handle, $oid) = @_;

    my $nBytes = 0;
    my $buf = "\0"x10;

    DeviceIoControl($handle,
                    IOCTL_NDIS_QUERY_GLOBAL_STATS(),
                    pack("L", $oid), 0,
                    $buf, length($buf),
                    $nBytes,
                    [] );
    
    return join "-", unpack("(a2)*", unpack("H*", $buf) );
}

my $key= $Registry->Open("LMachine/SOFTWARE/Microsoft/Windows NT/Curre
+ntVersion/NetworkCards/2",
                         { Access => "KEY_READ", Delimiter => "/" } );

my $adapterName = $key->{ServiceName};
print "Adapter name  = $adapterName\n";

my $hMAC = CreateFile("//./$adapterName",
                     0, FILE_SHARE_READ(), [], OPEN_EXISTING(), 0, [])
+;

for (
     [ "permanent" => OID_802_3_PERMANENT_ADDRESS() ],
     [ "current  " => OID_802_3_CURRENT_ADDRESS()   ],
    ) {
    my ($type, $oid) = @$_;

    my $mac = NDIS_Query($hMAC, $oid);
    print "MAC $type = $mac\n";
}
[download]

On my machine this prints (which is the same info that the mentioned C program reports):

Adapter name  = {0AA29800-521D-4B20-888F-9D3CB9E64E96}
MAC permanent = 00-0c-29-ee-47-65
MAC current   = 00-0c-29-ee-47-65
[download]

The cryptic network card name is being looked up in the registry. You might have to experiment a little with the lookup path (in particular the final "2", which is the card number). Good luck.