The HD4870 driver on WindowsUpdate works great, just doesn't support Catalyst Control Center. You use the regular Windows Display Properties to change the resolution.
If you wanted to change the AA and AF settings you can do that with RadeonPro, and after those are set you could even uninstall it + the settings will stay.
There is a way to manually install the Win 8.1 driver if you really wanted CCC for some reason:
1: run the installer but close it after it unpacks all the installation files to C:\AMD.
2: in Device Manager, under Display adapters, right click on the adapter and click Update Driver Software.
3: Browse my computer for driver software. Click 'Let me pick from a list of device drivers on my computer' in the next menu and Have Disk...
4: Click Browse on the pop-up menu and go to: C:\AMD\AMD_Catalyst_13.4_Legacy_Beta_Vista_Win7_Win8\Packages\Drivers\Display\W86A_INF.
5: Select the first .inf file - C7156445.inf - and click open, then select the model HD4870 from the list and click Next.
6: The driver should install with several screen flickers.
7. Now re-run the legacy driver installer with administrative privileges and have it install the Catalyst Control Center.
8. Restart the computer.
Note that the Driver Version installed this way is 8.970.100.0 from 24APR2013, older than the version installed automatically by Windows 10: 8.970.100.9001 dated 13JAN2015.
Note also that the HD4870 was the Radeon Fury of its day as the first card with GDDR5--which could not be clocked down at idle without blanking the sceen, so ran at full speed all of the time and idles at 60w.