As rahmu said, router is the best option.
However, if you don't have one, - or you don't want to use wifi on the second desktop -
You can enable Internet connection sharing on [desktop 1] and then you can easily connect from the laptop to the desktop 2.
That's a tutorial how to do it in XP ( I guess it's XP, I remember 169.54.X.X is the automatic tcp/ip addressing without dhcp for win2000 and xp )
Link
PS: I don't guarantee that it will work;
Back in old days I did it and it worked. ( I had one pppoe account and a switch, so I shared the connection on four computers and I could easily access them all remotely)
Edit: I have a slow connection, I couldn't see rolf's post before me, Bridging should work like a charm also
Bridge Connections