@SillySimmerGirl -- The first new PSU I tried is a Roseville Valens (but only 500W, as recommended on the GPU box); the one Installed today is the Corsair CX750M; and yes, I had to use the cables that came with the new PSUs since the old cables are permanently attached to the old PSU.

Beeps -- there are none; everything sounds almost normal as though the HDD is firing up, but then nothing happens as long as the new GPU is plugged in. I disconnected the 8-pin power cable and connected a monitor to the motherboard's VGA connection and it booted just fine, reconnected the 8-pin and again, only the sound of a hard whirring around but none of the clicks and such that would indicate Windows was doing anything.

After doing some research regarding the XPS 8300 and the Radeon R9 380, it seems the forum post @namaradus linked to does indeed identify the problem ... your new GPU is not compatible with your motherboard.

If I were you, I'd most likely keep the new GPU and PSU and get myself a new motherboard.

@namaradus -- Thanks for that link. More than likely that's the problem. Guess I'll be putting this card up on eBay soon since it's too late to ship it back to Amazon. I'll have to find a card that offers that dual UEFI deal.

If your able to build a PC or know someone who can
http://www.newegg.com/Product/Product.a ... 6813132513 Mobo
<a class="wiki_link_ext" href="http://www.newegg.com/Product/Product.a ... 6819113284" rel="nofollow">http://www.newegg.com/Product/Product.a ... 9113284</a> or <a class="wiki_link_ext" href="http://www.newegg.com/Product/Product.a ... 6819113285" rel="nofollow">http://www.newegg.com/Product/Product.a ... 9113285</a> Processor
<a class="wiki_link_ext" href="http://www.newegg.com/Product/Product.a ... 6811147242" rel="nofollow">http://www.newegg.com/Product/Product.a ... 1147242</a> Case

@namaradus -- I may build a PC someday, but for now my mission is to make this one my Sims 3 computer so I don't have to worry about what EA/Origin have done or may do in the future to control my use of the game. I dread the thought of ever having to re-download anything from Origin.

If your still on Win7 this one has been tested and should work with your computer according to Dell http://www.newegg.com/Product/Product.a ... -_-Product
It far exceeds the game requirements although you'll need too fiddle with the Graphicsrules.sgr