SharePoint 2010 Foundation problems encountered when doing a quick spin-up of a test instance.   

- Search service wouldn’t start
- Performing a search returned the error “Your search cannot be completed because this site is not assigned to an indexer”

To allow the search service to start the credentials assigned to the service were changed from Local Service to Local System.

To fix the “not assigned to indexer” error use Central Administration.

Navigate to “Manage content databases.”

Make sure you have the correct web application selected and click on the content database

Scroll down and find the Search Server section and select the search server from the drop-down