If there is any doubt about the health of hardware, I wouldnt introduce it to new hardware and take that risk. If I had a spare system that was healthy that I didnt care if it smoke showed, I'd try the card in that first before installing it into a new computer.
Also unless this videocard was one that was a gamers dream to own, I'd buy a new video card for the new system to make say an off the shelf $348 wallmart special desktop dual-core tower into a gaming computer. I would also likely have to install a more powerful PSU to go with the card. But I would also really look the computer over before buying it to make sure that it can take a universal power supply and is not a odd dimension PSU unit designed for this low cost computer, as well as make sure that this computer comes with a PCIe 16x slot for a video card to be installed to. With systems with APU's out there, you might find a computer that is low cost, low end, that is lacking key upgrade features, as well as if the APU is an AMD C60 you pretty much have a new computer that has the processing power of a 10 year old computer, but its GREEN due to much lower power needs than CPUs of 10 years ago!
I wasnt impressed with the processing power of the low cost Walmart computers although the prices were pretty good for anyone needing a computer that is new, and not for gaming out of the box.