Since I wrote earlier I have pretty much returned FSX to the impressive graphics I had before updating to Catalyst ver 13.9 (I am now using ver 13.4).
First thing to say is; if you have contacted AMD Technical Support I recommend tyou follow their advice and bypass my suggestions below. Second thing is; I am virtually certainly that you will not need to buy any new hardware.
What I suggest you consider doing is pretty straight forward - I hope you might find it not too daunting or difficult.
(Registry utilities these days are pretty reliable. Other people should feel free to jump in with their comments if appropriate!)
The process I did ... in simple steps ... was:
Uninstall the present Catalyst software (the driver for the graphics card and associated software e.g. the high definition audio for a HDMI connection). Using either the AMD uninstaller utility or another method such as the Windows software uninstaller in Control Panel, or CrapCleaner, or JetClean.
(When I used the AMD unistaller utility earlier it did not leave anything behind.) If you use something else or think it necessary then use something like CrapCleaner or JetClean to check the registry just in case there are any left over items which may conflict with the 'new' installation.
Reboot the PC. (The screen display will appear pretty basic whilst there is no dedicated graphics driver and it will look better when there is.)
Install the Catalyst version 13.4. (I stronlg suggest you simply accept the default options but make sure you select the "custom install" option to be sure all parts are included). Reboot the PC as prompted after the install.
(I use two or three freeware utilities, e.g. JetClean and JetBoost to stop unwanted programs taking resources and maximise the available RAM on the PC whilst I play(!?!) on the flight sim. I also disconnect the internet /network link and stop the antivirus too but I do not use any online addons).
Let me know if I should explain in more detail about what I suggest you consider doing and where to get the software utilities I mentioned. Do not hesitate to ask for more help either here or by contacting AMD Tech Support.
Don't be put off if something appears complicated, ask anything about even the simpliest things - there are many people around who will help you to sort out this or other problems.
(If you do then please give some basic details about your PC specification - in some cases it may influence what is suggested.)