I wouldn't jump to that comclusion yet. It wan't overclocked, so that certainly bodes well for it. I would move your soundcard down to your bottom-most PCI slot, as you said, and then look into buy a slot fan. They are rediculously cheap (around $5-$10US) and can suck/blow right onto your video card.
Does your video card have a fan? If so, which way does it blow (or is it even moving, that could be your problem irght there)? If it blows air out of your heatsink, then a slot cooler at lowish RPMs would be an excellent idea (it exhasuts the hot air right out of the case). If it sucks air in, then a coolr might not be such a good idea.
If the fan on your card isn't moving while the comp is on, try running farcry, if you feel comfortable doing so, get into the game (the actual gameplay, not just the menus), and then check the fan. Now, it MUST be running. If it isn't, then unplug the computer INSTANTLY, and call the company and see about a return. If after letting the card cool down to room temp, moving the sound card down, updating your video drivers, and possibly reformmatting your machine, and trying a different display, OR if the card does the same thign in another comp, then see about a retunr. If it's only a week old and never overclocked, they will probbly accept it and give you a new one, although I might ask for a refund and buy one from another company.
EDIT: Oh yeah, look at your mobo manual and see if running only 20 pins is OK. I know my ATX connector is 24 pins, but it is fine for me to run a 20 pin on it.
AGP won\'t fit in PCI-E... unless you use a really good hammer. ~Trotter