GIMP has the most horrible interface ever. I still use it like the sheep I am, though.
Alternatives include paint.net, and... well that's all I can think of at the moment.
The interface is hard to learn, but it's the only one with comparable features to PS. I'd probably recommend Paint.net to those who don't need all the features though.
If you are willing to - or doing work that can be done with - vectors,
Inkscape is fantastic. But then that's pretty much a different species. Better for some things (logos and similar graphic design work for sure) but you simply can't use it for most photo work.
I tried to do this, but I believe it may have been just for cropping.
It's pretty hard to tell what you are trying to do/use. I'd recommend just reading through the manual to see if that helps. You can't usually just pick it up and expect to use it.
EDIT: OK, I've just been trying this on a clean install on Win7.
Select an area.
To move the contents of that area, press alt, then ctrl. Click and drag then release ctrl (otherwise it will lock the movement to certain directions/steps).
To copy the contents of that area, press shift, then alt, then click and drag.
Note that what each combination does is stated in the status bar at the bottom of the window. It also gives you keys to try out, although it doesn't say what they each do.