If you set up the jobserver service to run as a user that can log into the database it should resolve the problem. The SYSTEM, NETWORK SERVICE, and LOCAL SERVICE users typical of services don't generally have access to the databases. A quick simple test of this would be to set it to run as your user, restart the service and try to execute the job. If it works then you could create a "SERVICE" type of account with access to the database and configure the service to run as that user.
Hope that helps.