From the very palpable steps available in solving it only one step seems to be easier than the others. That is, going for the old Skype installation package. It is recommendable to forage among many old Skype versions online to do that than go for the most recent one in other to be abreast of some Skype features. If you aren't comfortable with the use of aging versions of Skype, at least as a last resort, it would be advisable to download the d3d9.dll from the internet and extract it to your System32 folder. Before downloading the file, make sure you have a better idea of the link authenticity, for security and privacy purposes. Nevertheless, taking the time to look for trusted sites is rewarding for the efficiency of a system as well as for the safety of important files against malicious attacks.
Some information about d3d9.dll, which stands for Microsoft Direct3D direct-library link is said to be pertaining to system network security while on the other hand it is used by Windows during graphic in DirectX. It is asserted that Windows can hardly function properly without it and Skype that needs it for its functionality. From database this file seems to be assigned to Microsoft system 32 folder and it shouldn't be removed from there for whatsoever reason.
Step 4: If after all you are still getting the same problem this would solve it by downloading Windows installer 3.1 from Microsoft website