or, i just noticed this today, i just rebuilt PC1 (sig) again..and was looking at the power supply bracket. now heres the good news: you might be able to still use your current case, and just throw another psu in there, it will just be one mounting hole short, bad news: i think the mount is upside down, plus i think that a quality psu will be too long to fit in the case.
thats if you plan to keep the current case. for building it: yes you are correct, unplug the computer, and find a suitable work surface, NOT CARPET!!! a desk or counter should do just fine. Unplug everything from the outside of the case, and open the case. touch something metal inside the case, like a bolt or screw, to ground yourself to prevent against ESD (electrostatic discharge). Now using the picture that i provided earlier that has the mounting locations of screws for the motherboard, and get a screwdriver or socket, or Allen wrench (depending on what it is) and remove all the screws, after of course you have disconnected all wires from inside the case that go to the motherboard. before you disconnect the front panel connectors (switch, pwlight, hddlight) trace them and mark which ones are which, makes assembling it much faster. now remove your motherboard, hdd's, cd drives, etc...
Now on the new case, and use
this tutorial to help assemble your computer. now would also be the time to dust you components off, as they were pretty dusty.
Just remember, don't change any jumpers and plug everything back into the places they are originally from. if done right, then it should start up like nothing happened.
(i made that mistake today, i accidentally got my ide cables backwards and plugged a hdd into the sec ide channel, and a cd into the primary and got a boot error...man that was funny to work out, looked inside and bam there it was, yellow cable was in blue port, and blue cable was in yellow port. lol.
and one more thing (yea i know i go on forever), if you purchase a case with a side window, take a good 20min or so and survey the inside of the case for good hiding places for your wires, because wires sitting in the middle of your window looks like straight crap (click link in sig that says hp pavilion 7940, its like the second and third pictures down on the first set on the right) its also a kinda good tutorial, just not as detailed. if i wanted it to be a tutorial, i would have taken more pictures...