1) It has an Intel G35 Express motherboard chipset,http://en.wikipedia.org/wiki/List_of_intel_chipsets#Core_2_chipsets
Under the - Chipset heading on the left, scroll down to - G35
Note that under the - Graphics heading, all the way to the right, that the Intel G35 Express chipset;
1) Will support a PCI-Express x16 expansion slot. This means a PCI-Express graphics card can be used, IF, there is a PCI-Express x16 slot on the motherboard.
[ PCI-Express is a technology. The current PCI-Express technology is PCI-Express 2.0
There is a PCI-Express x1 expansion slot, and a PCI-Express x16 expansion slot. (Not relating to Your computer at the moment)
The PCI-Express x1 slot is Not used for a graphics card.
The PCI-Express x16 slot IS,http://en.wikipedia.org/wiki/PCI_Express
2) Has Intel GMA X3500 Integrated Graphics.
Meaning if there is NO graphics card installed right now, the computer is using Integrated Graphics, (Intel GMA X3500,http://en.wikipedia.org/wiki/Intel_GMA#GMA_X3500
Now,...you are essentially working on a laptop with a touchscreen.
Once you remove the 10 screws from the Back Cover, and remove the cover, you are looking at the exposed circuitry of the computer.
You NEED to follow Anti-Static Precautions. This cannot be performed as on a regular desktop computer. Touching the metal frame (Of the unplugged from power computer) will do you No good.
You need to use an ESD wrist strap, and connect it's alligator clip to a good ground source. [ Electro Static Discharge]
Your body carries Static electricity. Static WILL fry out (Short Circuit) the delicate hardware components inside a computer.
With the Back Cover off the manufacturer knows all of the hardware components are exposed. This means the person working on the computer should be aware of Static issues, and use proper tools.
The average consumer is not aware of this. This is why only a ram memory upgrade is recommended by the manufacturer. (Before they went out of business)
This is why there are no service manuals released, also.
Only for the qualified authorized service techs.
So,...let's look together. See if there is a PCI-Express x16 slot, for one.
It can be any color. Will be longer than any other expansion slot on the motherboard. The PCI slots (Usually white) are not as long.
(164 contact pins. 82 on each side)
These examples of a PCI slot, and versions of a PCI-Express slot, are all the same color. (Yellow) Not usual for a desktop computer.http://en.wikipedia.org/wiki/File:PCIExpress.jpg
The top example is an example of a PCI-Express x4 slot.
Hardly EVER used, I didn't mention it.
Has 64 contact pins. 32 on each side.
The next slot down is an example of a PCI-Express x16 slot.
164 contact pins. 82 on each side.
Next down is an example of a PCI-Express x1 slot.
36 contact pins. 18 on each side.
Next down is another example of a PCI-Express x16 slot.
Last example is an example of a PCI slot. TOTALLY different technology than PCI-Express.
124 contact pins. 62 on each side. (Unless PCI that is 64-bit)
IF, there is a PCI-Express x16 slot on the motherboard, you can use PCI-Express 1.1 or 2.0 graphics cards.
You need to be concerned with;
A) How much height is available for the graphics card, and how much length? Check the measurements inside the computer. Match to dimensions of the graphics cards you are looking at.
B) How much POWER does the graphics card require? It's in the Minimum Requirements stated for the graphics card.
How much power is available to the all-in-one computer?
This could be an instant stopping block.
AMD ATI Radeon graphics cards generally use less power, than a comparable Nvidia graphics card.
C) Worried about your computer per se uses DDR Sdram ram memory, and the graphics card uses GDDR3 ram memory? (Just an example. Not directly related to Your computer)
Don't be. Doesn't matter what graphics memory a graphics card uses.
The graphics card does Not rely on the system resources (Processor and Ram Memory) of the computer.
A graphics card has it's own Processor, (GPU. Graphics Processing Unit), and graphics ram memory.
For additional questions, or to have me explain in further detail, or to clarify, post in a Comment.