First off, while you are resolving installation issues, you can use a portable install of Radian. If you already had Radian installed and activated, you can just unpack the portable install archive and run from there. You won't have MAP file associations and if you want to use the ODBC driver, you have to register it manually, but that's about it.
On to the installation issue - it would be helpful to see the log file. You can capture the log file by installing using the following command line - open a command prompt with Administrator privileges:
msiexec /i manifold-9.0.159-x64.msi /l*v log.txt
The log file is going to be written into log.txt.
I suspect the problem is in the post-installation step which attempts to launch Radian binaries - and they refuse to launch. This might mean that you don't have the installation prerequisites installed (like Tim says, although if you already had Radian installed before, perhaps that's not it), or that some of the files were blocked by an antivirus or a similar system scanning tool. To be sure it is not the latter, turn all antivirus-like tools off before trying to install. (To be sure the install is safe, verify its hash sum, as explained, for example, here - see the discussion on SHA checksums.)
Hope this helps. If not, contact tech@, they will work it out.