Problems after migrating the ConfigMgr database

At a customer location ConfigMgr was installed on a SQL cluster. ConfigMgr was running fine, and Reporting services was installed on a single node. All went fine. After a few months customer deciced to break down the SQL cluster and migrate databases to single servers. The ConfigMgr database is migrated with help from MS TechNet: Manage Site and Hierarchy Configurations
 
All seems okay after the migration. The ConfigMgr console can be started and no direct errors are seen. After a week looking in the configuration, multiple errors are seen in the logfiles:
 
CCMSETUP.LOG (from a client)
- GetDPLocations failed with error 0x87d00215
- Failed to get DP locations as the expected version from MP "SCCM Server". Error 0x87d00215

CERTMGR.LOG
- Error: Failed to write certificate from server (SQL SERVER\TrustedPeople).
- ERROR: Failed to open certificate store (HRESULT=0x5)

HMAN.LOG
- SMS-Site-S01 could not be created, error code = 8203.
- Failed to connect to remote WMI repository on machine "SQL Server"
ConnectServer(Namespace) failed. - 0x80070005

POLICYPV.LOG
- Failed to sign Policy Assignment, Error code = 0x8009200b
- Error signing policy assignments (0x80004005).

Also multiple errors are seen in the ConfigMgr console:

SMS_HIERARCHY_MANAGER
- Configuration Manager cannot create the object "SMS-Site-S01" in Active Directory
- Hierarchy Monitoring detected that the SQL Server machine certificate has missed. It is failed to remediate with Error.
- Hierarchy Monitoring detected that the SQL Server machine certificate has missed.
 
SMS_SITE_COMPONENT_MANAGER
- Site Component Manager failed to reconfigure site system "SQL Server" to receive Configuration Manager Server Components.
- Site Component Manager could not access site system "SQL Server". The operating system reported error 2147942467: The network name cannot be found.

SMS_POLICY_PROVIDER
- Policy Provider has failed to sign one or more policy assignments. It will retry this operation automatically.

Does anyone has a clue why communication to the ConfigMgr database fails? It seems to be something with permissions, WMI and certiticates. Also reporting isn't functional anymore. ConfigMgr computeraccount is an administrator on both ConfigMgr and SQL Server. Site Reset didn't help me unfortunately.

Update 30-1-2013: Solved with assistance from Stephan Wibier (@StephanWibier) Thanks!

Update 15-5-2013: The trick is to re-create the certificate which is needed for communication between ConfigMgr and SQL Server. Then everything will be okay again. Just follow steps from this blogpost for the permissions needed: "Fail to create SQL Server Certificate" during installation.

As described on Microsoft TechNet also a new self signed certificate is needed which much be assigned in the SQL Server Configuration Manager / SQL Server Network Configuration / Protocols for MSSQLSERVER. Hope it helps!