Welcome To Tomshardware, OP.
There is no such thing as matching graphics card to a motherboard. A Motherboard acts as a basement in which you can build your rig in your favorite taste. It does not play any role on increasing the gaming performance. The only thing that should match is CPU and the favorable chipset motherboard. If you are using AMD processor, your motherboard should be amd-based chipset like Asus M597 FX, M599FX Pro R2.0, and so on; otherwise, it has to be Intel-based chipset board like Gigabyte H87M-D3H, Gigabyte B85, and so on. It pretty much seems that you own an Intel Processor as I could see the current one is an Intel-Based chipset motherboard. If you cannot view the display, there are few reasons.
First, Make sure you've connected the cable to the graphics card port and not into the onboard video port i.e., The cable should be connected to the graphics card only. After that, load optimized defaults in your motherboard BIOS so that the location of the video card (PCI 1 or PCI 2) will be automatically detected. If you are not sure on how to enter BIOS, switch off the computer, remove the power plug from the CPU, open up the case, and remove the CMOS battery; After then, insert it back again, get all the cables back to the respective ports, and turn your computer on. Here, the monitor should display "Your BIOS has been reset" and from there, you can see an option to load optimized defaults and I want you to select it right away. Now the display should work.
If the problem persists even after following these methods, you must make sure your graphics card has enough power from the PSU (Power Supply Unit, which distributes the exact power needed for each component). For Radeon HD 4870, a minimum of 430 W PSU is required. To be on safe side, 500 Watts PSU will be better.
As you already own a 650W PSU, the problem must be definitely on your card. Test it on a different computer. If it works in other system, the problem might be in your motherboard's video card slot yet it shouldn't be the case for you unless you have physically damaged it.
That's all. Hope it helps.