Chances are that is the Trojan. There is no file in 2k/xp that is named desktop.exe. The versions of Windows that may have it are pre-98 ones. The file that controls the desktop is explorer.exe.
What you have to do is start your computer in safe mode (just click the F8 key a lot while your computer is booting so it brings up the option screen,) push ctrl-alt-delete and make sure desktop.exe isn't listed on the processes and then proceed to do a search on it to delete it. It would also be a wise choice to run any virus/adware detection programs while you're in safe mode.
oh, its a nice day. TO EAT CHILDREN!!!