I've got an old dead NES at home, since the 750ti has been released, at 60 watts, I've been considering doing something awesome. I know there is not much space in the case so I was thinking something like this, at least size wise, for the psu http://www.newegg.com/Product/Product.aspx?Item=N82E16817338063
a shorter heatsink than the stock one like this one http://www.newegg.com/Product/Product.aspx?Item=N82E16835103177
A mini itx motherboard, an amd AMD Athlon X4 740/750k/760k for the cpu, something cheap that has 4 cores, 8GB of normal ram with low heat spreaders, and of course a 750ti for the low power usage gpu. No optical drive because I don't use them and I have a usb one IF I ever need one.
Would this be feasible?
http://www.instructables.com/id/Build-a-Nintendo-NES-PC/
You could try a sfx power supply that may fit. http://www.scan.co.uk/products/450w-silverstone-sst-st45sf-g-strider-sfx-modular-80plus-gold-psu
Sure. Been done plenty of times, though usually with emulators in mind rather than true PC gaming.
There's enough space for an ITX or a small Micro ATX board (about 8" x 9" at the base). Of course, there's not enough vertical space to have a graphics card. An NES is less than 4" tall. So you'll probably need to go APU or possibly a 90 degree PCI-E bracket if you really want to cram a GPU in there. Not sure you could find a sufficiently powerful PSU that would fit though (the one posted above MIGHT fit, if you can find a good spot for it), so you may have to go external.
Your biggest issue is obviously going to be heat what with a MB, Heatsink, GPU, HDD/SSD all crammed into that small of a box, so make sure you vent her.