On a recent 2013 Foundation install, I had a recurring problem. The client wasn't willing to give the installation account full SA privileges, so we asked for the dbcreate role and thought it was enough (hint: it's not). Make sure you add the securityadmin role as well.
If you don't, you'll probably end up with an error like "The search service is not able to connect to the machine that hosts the administration component". In Standard or Enterprise, you can rip out the offending service and add a new service application, but Foundation is a bit more black-box in its limited-functionality approach. To resolve this error without a complete reinstall, I did the following:
1) Ensure that the securityadmin role has been granted.
2) In Central Admin->Application Management->Manage Service Applications, select the Search Service Application and delete it.
3) On the SharePoint SQL Server box, delete all databases with "Search" in the name.
4) Rerun the SharePoint Products Configuration Wizard.
At this point you should have a working Search Service again.