I can't speak for the third party software, it is possible that it has disabled the service - you may want to uninstall it or find out the reasons in case they conflict with each other.
However, to enable a disabled service, all you do is:
Go in to computer management, (Click the
Start Orb > Right click on
Computer > Click on
Next, go down to
Services and Applications >
Services and look for
Windows Search Service
Make sure that this is set to
Automatic (Delayed Start).
Edit based on comments.
I have no idea why the service would not be there if it is installed correctly. At your own risk, you can recreate the service by typing the following at a command prompt:
SC create WSearch binPath= "C:\Windows\system32\SearchIndexer.exe /Embedding"