ATI Mobility Radeon X1600 graphics card Windows 8 driver missing

Question

I just installed Windows 8 Enterprise Trial version on HP nx9420 laptop (2GHz dual core prosessor, 4gb memory, ATI Motility Radeon X1600 graphics card with 256mb own memory, 1680x1050 native display resolution) on second partition, side by side with existing
Windows 7. 
Installation succeeded perfect, except Windows 8 couldn't install, nor did find from Windows Update display driver for ATI Mobility Radeon X1600 graphics card. Only Microsoft generic display driver was installed and it offered maximum 1450x800 resolution,
so not laptops native 1680x1050 screen resolution. 
Windows 7 can install working ATI driver right from Windows Update for that graphics card (version 8.561.0.0 dated 1.12.2008). 
Laptop manufacturer HP has latest, old driver for Vista (version 8.453.0.0 dated 22.1.2008), so I installed that, selecting compatibility mode Vista with setup-program in Windows 8. That installed, but seems to have some problems, telling of missing library,
maybe with some ATI extra diplay manager software and C++ 2005 library, that it installed. 
MY QUESTION: Is there some problems with Windows 8 and that ATI Mobility Radeon X1600 graphics card? Why isn't the Windows 7 -version of ATI mobility radeon X1600 display driver available in Windows Update for Windows 8 too? 

Answer 1

Thank you all of your thanks. 
I can confirm that this solution works with Windows 10 Technology/Insider preview too. And surely works with forthcoming Windows RTM too. 
Windows 8.1 and Windows 10 TP work both like a charm with nearly 10 years old HP Compaq nx9420 laptop, with Intel Core 2 Duo and ATI Mobility Radeon X1600 display adapter. Nice co-operation of "old" hardware and very Modern Windows OS.
So in brief:
If you have laptop with ATI Mobility Radeon X1600 or other X1000-series display adapter and
you want to install Windows 8, 8.1 or 10, do this:
0) First just install Windows 8.x/10. It will install Microsoft Generic display driver, but that doesn't support full resolution of ATI Mobility Radeon X1000 -series - for example it may show maximum 1400x1050 -resolution, thus your laptop display and Radeon
X1000 may support native 1650x1050, but you can't obtain that resolution with that Microsoft generic driver. So you need ATI-driver and you can get it this way: 
1) With Internet Explorer (this doesn't work with other browsers) go to
Microsoft Update -catalog:   http://catalog.update.microsoft.com/
2) Search "ATI Mobility Radeon X1600"
  (or X1300, X1800 etc)
3) Sort search results by date (last update -column), latest on top. You will see drivers for Windows 7
- they will work with Windows 8.x and 10 too. There is certainly two of them; other is 32 bit only and other is 64 bit dirver.
4) Select proper driver version of them, according your Windows 32 or 64 bit, so click Add
5) At top-right click Show basket and then download those driver packages to your computer. They are cab-file
-packages. 
6) Obtain 7-zip -utility, install it and with it unpack that cab-driver package on folder with its package-name.
7) On start of taskbar, right mouse button click Windows-Start and then select Hardware management. On
Hardware management -window open Display adapter -section, then mouse right click Microsoft adapter and select Update driver. Then on next window, select search driver from computer. 
8) Browse on folder, where you unpacked ATI driver (on stage 6 earlier) and select Next ... that updates
driver, on the go and you don't need even to reboot Windows. 
9) Now you have proper ATI Mobility Radeon -driver in use. It  surely sets automatically resolution
according your laptop screen (so recommended native resolution of screen panel) or you can select that on diplay settings. 
Extra: For that Windows 8.x/10 boot works fine too, do this too: 
Seems that Windows 8.x (and Windows 10 too), with their hybrid-shutdown -functionality, require some support of the display adapter, that ATI Radeon Mobility x1000 -series don't have. 
So the solution is to disable that Windows 8.x (or Windows 10) hybrid boot -functionality (that is quicker boot) and to use "normal boot". 
You can fix that this way:
- at end of Taskbar click battery/power icon and select Power settings
- navigate to power and sleep settings
- either at bottom of those settings, or in Win10 more power settings, select power buttons functionality/settings (so what power button, sleep button or closing laptop screen does)
- at bottom of those settings is shutdown options (or with similar name). uncheck "use quick boot" -settings (for to uncheck that you may need to click first upper "changing disabled settings" (or similar name) at top or windows) 
(I recommend to check Hibernate at the same time too, because that is usefull)
- then Save settings and reboot Windows and you have got rid of that problem that Windows 8.x/10 don't show Lock screen, now it does.
Boot takes just a little longer, so practically no problem. And if you need quicker boot with laptop, use Hibernate-state, so don't shut down your laptop, but instead put it into Hibernate-state (that is better than Sleep mode, because Hibernate-mode doesn't
consume battery-power, like Sleep-mode does)