I have the Remote Desktop Connection installed on Windows 7 HP, but when I type in the full server name of my Windows Server 2003 box, it fails to connect. Can I fix this, or do I need Windows 7 Pro?
The issues you're having are not due to the client OS version you're using.
Give us some more information about your setup and we may be able to help you get to the bottom of it.
Here are a few ideas to get you started: