Does Acer computer corporation give partial refunds if the computer you bought from them isn't working properly?

only within the warranty period.

If you recently bought this computer (less than a year), it is still under warranty so you should bring it to their service center. You are entitled to a direct replacement if it's still under a week old. Longer than that is free service and maybe parts. The fact that you have opened the computer to reseat the video card may have voided warranty though especially if there are warranty seals broken. 

Anyway, you already know the problem. Take out the video card, wipe the gold contact points with a clean pencil eraser, put it back in place and rock the card slightly and gently from side to side after you push it fully in place. Make sure the locking clip engages and you screw the backplate firmly (not too tight though to cause a loose thread). You might also find that positioning the backplate tilted on one side might do the trick.

typically, they might ask you to exchange it for another. they don't do refunds.

the exception is, if the video card was something you added after, and did not come with the computer. they don't support aftermarket modding.

No.  If that were the case, thousands upon thousands of people would be contacting them to request a refund.

How do Acer know whether YOU know what you're doing with computers?  For instance, it MIGHT be a simple setting that needs to be changed on your computer to ensure that the video/graphics card works efficiently.

If it's still within its guarantee period, you could ask Acer to take a look at the computer as YOU believe that you've identified a fault with it.  Acer would then take it in, have a look, and determine the best course of action to take, which COULD require replacing the 'faulty' part, or even replacing your whole computer if so required.