You could buy a cheap case,some even come with a power supply,look on newegg,they have some good deals. you could put your computer parts in a new case yourself
Sounds like it needs another motherboard, but someone else might have more ideas.
Also if you can get a similar motherboard,then you can reuse the rest of the parts.
Take out the videocard before installing windows, thats so the drivers for the board/usb and onboad video drivers will get installed. if you have the video card in the computer when windows is installed the usb port drivers might not get installed.
Install windows on another harddrive, clone that harddrive and copy to usb harddrive using acronis true image(it clones fast), then set harddrive boot order in bios to boot from usb and disconnect other harddrives.
Since the Dynex works and the Corsair does not,maybe they sent the bad one right back to you by mistake,try the corsiar one in another computer,if it still doesnt work then its another bad one.