you pass a wrong string to the Win32::AD::User. There is no need in additional ',user' strings you add here:

my $adstring = join('', $user, ',user",',$user, '"');
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It works in my environment with:

my $acdiruser=Win32::AD::User->new('WinNT://dnsdomain.com/',$user);
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and

my $acdiruser=Win32::AD::User->new('WinNT://NTDOMAIN/',$user);
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you can print out all available properties using $acdiruser->print_me(); I'm not sure if it depends on my limited rights the property _LDAPAdsPath: which I expect to contain the DN attribute is empty for me :-(