A GeForce GT 610 needs 16 amps on the 12v + rail and a 300 watt power supply , no additional PCIE power connections are needed.
Being a single-slot card, the NVIDIA GeForce GT 610 does not require any additional power connector, its power draw is rated at 29 W maximum. Display outputs include: 1x DVI, 1x VGA, 1x HDMI. GeForce GT 610 is connected to the rest of the system using a PCIe 2.0 x16 interface.
https://www.techpowerup.com/gpudb/821/geforce-gt-610.html
It may even run on your current setup.
Processor Intel(R) Core(TM)2 Duo CPU E8500 @ 3.16GHz
Manufacturer Intel
Speed 3.2 GHz
Number of Cores 2
Video Card 1 Intel(R) Q45/Q43 Express Chipset (Microsoft Corporation - WDDM 1.1)
Manufacturer Intel
Chipset Intel(R) Q45/Q43 Express Chipset (Microsoft Corporation - WDDM 1.1)
Dedicated Memory 64.0 MB
Total Memory 1.7 GB
Video Card 2 Intel(R) Q45/Q43 Express Chipset (Microsoft Corporation - WDDM 1.1)
Manufacturer Intel
Chipset Intel(R) Q45/Q43 Express Chipset (Microsoft Corporation - WDDM 1.1)
Dedicated Memory 64.0 MB
Total Memory 1.7 GB
Memory 8.1 GB
Operating System Microsoft Windows 10 (build 10240), 64-bit
Service Pack 0
Size 64 Bit
Edition
Display Maximum Resolution 1366 x 768
This is a basic run-down of my system at the current time. I am attempting to do more work to it but at the moment I just need a graphics card somewhat better than my current. Let me know if this changes anything or if it sheds more light. Thanks again!