You attached graphics were a NO show. An educated guess, if the card fits the slot, yes, otherwised DO NOT force it.

those were links to:

VisionTek - ATI RADEON HD3870 OC 512MB GDDR4 PCI Express Graphics Card
Model: 900226 | SKU: 8762234

Gateway - TV Desktop with AMD Phenom™ X4 9500 Quad-Core Processor
Model: LX6200-01 | SKU: 9031692

both are on bestbuy.com

the card is a pci express card and there is a pci express slot open on the computer, but that is not what I am concerned about. I am more concerned with drivers, software, and somewhat with cooling and power supply.

Then it's a non-issue. Drivers, etc. will come with the card. Unless the retailer gives you some reason to think otherwise any cooling device will come with the basic unit.

The power supply is the only issue I would wonder about. The card specs say it requires a 450W or higher power supply and that Gateway model has a 400W. You may be just fine though.

Yeah. Also bear in mind gateway, dell ,etc... use quite nonstandard cases. An upgrade power supply *should* fit and will probably be required. Dont know about the card you mention, but many require additional power cables which generally arent part of stock power supplies. Also bear in mind that if your case is nonstandard the PCI-Express slot may be designed in such a way that a very wide/long card (particuarly one that takes up 2 slots due to a fan) will not fit.