Microsoft Search - should be started
IPSECServicesPolicyAgentCiSvc - should be started
Routing and Remote Access - only started when required
Performance Logs and Alerts - only started when required
What happends when you try to start the two services?
For so many files missing you would have to suggest the system is infected in some way. What anti-virus did you scan with?
Is there a backup?
Try malwarebytes and run a full scan.
http://www.malwarebytes.org/mbam.php