I am trying to install the latest version of DirectX from Microsoft but I get the following issue. Any ideas?
First run services.msc from run box in start menu. Then in the list check that Cryptographic Services are running. Also, to be safe, set it to automatic.
If the problem isn't solved, go here and download newest version of DirectX from there. Another option is go here and download websetup. Run this program every two or three months or so and it will download and install newest version of DirectX. Also it only downloads updated files so it transfers less data.
If all fails, it could be that you have problems with Internet connection (bad router, modem etc.), problems with RAM or a virus.