406 electrical fault (I hope)

The door courtesy lights are staying on, even after the engine has started. They flicker and eventually fade out after what seems a long time. The interior lights also stayed on but those can be manually switched off. That's the first problem but also I feel connected the remote central locking and deadlocking also has ceased to work. Fortunately the doors lock with the key, this also kills all the interior lights. All thought and advice gratefully welcome.