sofar looks like you have only a 300 watt psu. Not shure if your case will take a standard PSU. But I did find this http://www.cputopia.com/psu-replacement-gate-gateway-dx4320.html
For your own good, leave that PSU where it is and run far from it. Gateway PSUs are
not designed to handle high-powered graphics cards and will be a time bomb waiting to explode if you try playing Skyrim with a 560. I wouldn't even build an HTPC with that in it.
Every component in your computer will depend on the PSU for
correct and sufficient power. When your PSU is insufficient or failing, it can malfunction and cause anything from instability (if you're lucky) to permanent damage to any of your components (usually the video card). It's important to select a high-quality, 80+ Bronze-rated or better, and high-wattage unit if you want to have a powerful video card in your computer. A good rule of thumb is to add 40% to the recommended wattage for your video card.
Excellent buy:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139020
$75 for that high-quality unit is a great deal and it can handle nearly any single video card you want to install
reliably. 650w is a little overkill for something like the 550 Ti but there's nothing wrong with being extra safe, not to mention that PSU will last you through multiple upgrades for some time to come (and has a 5-year warranty!).
Here's a couple of recommendations for video card:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814125410
http://www.newegg.com/Product/Product.aspx?Item=N82E16814121419
Both have excellent price/performance ratio. Depends on your budget. Between the 550 Ti and the TX 650, the total with shipping in my cart is only $203.
BTW if you need a better case, good cases are cheap. I use this one:
http://www.newegg.com/Product/Product.aspx?Item=N82E16811147023&Tpk=blackbone
and I know a few shop owners who've used dozens of this one:
http://www.newegg.com/Product/Product.aspx?Item=N82E16811119227
Both great options that come with solid cooling.