Difficulty connecting with Remote Desktop

Note: Although the target machine is virtual and within Hyper-V I do
not believe this has anything to do with the issue as you will see.

I have two virutal servers in Hyper-V. One is accessible remotely from
my Vista Ultimate machine and the other is not. I cannot find the
problem.

Here is how both machines and connections are similar:
• Both are installed with the same O/S - Windows Server 2003 R2 Ent.
x64 SP2.
• Both are configured to enable Remote Desktop.
• Both are members of the same Domain.
• Both machines have the same memory.
• Both reply with a ping, name and IP address.
• Both are configured with the same role: Application Server (IIS).
• Both RDP shortcut configureations are the same, but for target
computer name.
• Both are connections are configured with the same administrator
account.
• The same remote computer (Vista) is used in attepts at remote
connection.
• Both machines accept login with this administrator account from
within the Hyper-V machine.
• Both remote computers are running.
• Both machines are otherwise idle - no other users - no processes
running.

Here is how the machies are different:
• The machine that accepts remote connection (A) has SQL Server 2005
installed.
• The machine that does acceot remote connection (B) has SQL Server
2008 installed.

Here are the things have checked out;
• Attempts have been tried over time with the same results.
• Memory is not the problem.
• Using the IP address instead of the name does not work.
• The network is not the problem - it works for one of the machines.
• The firewall is not blocked
• The machine is visible - a ping receives a proper reply
• Remote connections is enabled on that machine
• The account being used is valid on that machine
• The remote computer is not asleep or hybernating
• The remote coputer is not busy

What else is there?

Here are the characteristices of the connection process for each
machine;

Machine 'A' (connectable)
1.) I click on shortcut for machine 'A'
2.) Remote Desktop Conection dialog opens
3.) I click on "Connect" button
4.) 2nd Remote Desktop Conection dialog opens saying "The identity of
the remote computer..."
5.) I click "Yes" to button
6.) Small "Connecting" box with "Cancel" Button opens...and quickly
then a window having the RDC and login appears for a successful
connection

Machine 'B' (not connectable)
1.) I click on shortcut for machine 'B'
2.) Remote Desktop Conection dialog opens
3.) I click on "Connect" button
4.) Small "Connecting" box with "Cancel" Button opens... and
lingers... (I never see the logon screen)
5.) Error is returned.

The error:
--------------------
Remote Desktop Disconnected
--------------------
This computer can't connect to the remote computer.

Try connecting again. If the problem continues, contact the owner of
the remote computer or your network administrator.
[ OK ][ Help ]
--------------------

What could is the problem?