I searched the web and found the best solution to be found here.
Becasue there are several fixes on this blog I have included the part that works for me:
Thanks,
Rahul
Basically SharePoint install deletes and recreates the registry entries for these Services and assigns Local Service Account . This account does not have the necessary authority and therefore stops. You need to change the services to have the correct account type inflight, when it stops at installing the two services...
There are two Services that this applies to:
SharePoint Foundation Search Service and
SharePoint Search Service
This caused me hours worth of issues until I found the post as noted.
regards