Sorry I forgot to say that I used the SQL Server Native Client 11.0 to recreate the System DSN.
I deleted both System DSN and retry to start the service : same error.
Could it be an issue in the registry? Here is the key that was changed :
HKLM\SOFTWARE\VMware, Inc.\VMware VirtualCenter
- DbInstanceName : sqlserver\sqlinstance
- DbServerType : Custom
HKLM\SOFTWARE\VMware, Inc.\VMware VirtualCenter\DB
- 1 : SQL Server Native Client 11.0
- 2 : domain\user
Thank you.