Don't give up yet. I have a +10 year old computer with an ATI/AMD HD 3780 X2 on a 1511 Windows 10 OS (I thinks that's the second build) and I managed to run it as intended. I think I'm using an old customized driver since latest ones dropped support. I never connect it to the internet and manage it some other ways when I have to so newer nonsupporting drivers don't find their way thru automatic Windows Update.
I put it at my cousin's home next city where we gather to play games on it so I can't check right now. Just yesterday we played Trackmania on it for hours and it ran very well. But my point is that if the 3780 X2 worked, there is a chance your 4870 works too, hopefully if newer Win 10 builds doesn't screw it even further.