ThomasLeong :
That is an unusual arangement of monitors you have there. I have only tried with a normal linear arrangement, eg. 1,2,3,4 in that order, using Gefen's DVI Dr. If you can wait a few days, I'll try a non-linear arrangement when I get to office next week.
The Gefen DVI Dr. is an EDID Manager device that connects between the source (gfx card output) and the monitor/projector. Similar devices are available from Lightware, HDFury, DVI Parrot. Some of them have HDMI versions instead of DVI - Gefen and HDFury. You need one EDID Manager for each output - four in your case. There are also software-based EDID emulation with AMD's Catalyst Pro used by AMD's professional range of workstation gfx cards, and perhaps also with nVidia's pro range.
Basically, the EDID Manager locks the monitor's EDID information and sends that on to the source such that unplugging, and re-plugging cables do not trigger a reaction from Windows to re-configure its output(s). It is essentially tricking Windows and the gfx card that the output is always connected, even though it may not actually be.
Thanks; however the reasons I want to be able to connect and disconnect my monitors in Windows are so that
a) the system doesn't waste any resources on my pretty animated wallpapers that I can't see and
b) my mouse cursor doesn't wander off into a place that makes it difficult to find again
c) I can put any one of my monitors into stand by with a keyboard combination (e.g. Win + M + 1)
e) Windows doesn't put any windows that I open on monitors that aren't actually operating at the time
Wouldn't tricking Windows into thinking the output is connected prevent those?
Also, I don't really want to pay for hardware when I feel like this should be something really simple for Windows to just remember where my monitors go. There is actually a software program called "Display Changer" which is meant to be able to set the monitor positions by command line which I could then add to my keyboard shortcuts but that program doesn't work most of the time (and when it does, it only puts on monitor in the correct place) so it's of no use.