Wait, if you didn't have a Mac before, and the eMac is your only Mac, then what is hooked up to the HP display?
I don't think that it can be the eMac since both the screens have different docks.
Hackint0sh?
EDIT: I looked closely and saw that the window on the HP has the Close, Minimize, and Maximize buttons in the top right. So I'm guessing that the 'dock' is actually the wallpaper?
No, I use RocketDock. Its works just like the OS X docks, but its for windows. The Gateway monitor is connected to the same computer that the HP is connected to. Dual Monitors.