I had the exact same problem where any time I tried to install a program, I got the error message "windows installer service could not be accessed", but none of the fixes I found online worked.
After tons of trial and error and banging against the wall, here's how I fixed it:
1. I went into the windows registry to the [HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\msiserver] path.
2. I changed the ImagePath value from "%SystemRoot%\system32\msiexec /V" to "C:\Windows\system32\msiexec /V"
3. I went into my windows services (services.msc) and stopped and started the Windows Installer Service. I also set it to start automatically.
4. I rebooted my computer.
5. Problem solved!
Essentially, for some reason or another, I had to hard-wire the path to the msiexec executable to the C:\ drive instead of using the dynamic %SystemRoot% variable, and that fixed it for me.