Hook the systems together via a router and a couple of ethernet cables. I would use a program like Dameware Mini Remote Control to visualize the desktop as mentioned above. The advantage of Dameware is that you can remote install the software on the target once you get the IP address. You will need to use a user account that has admin on the target system.
This is a bit involved so I have to ask what is the purpose of getting to the desktop? If it is just to copy over files the it would be easier to pull the hard drive from the old system and put it in an external USB enclosure. You can then copy whatever you need.
http://www.dameware.com/