Is it permissible to use an old, unused government-owned printing machine found at home for personal need?

If the aforementioned machine is held by your father as a trust, you are not permitted to use it except with the permission of the competent authority. This is because such an act would constitute a breach of trust and an unlawful appropriation of another's property. The justifications you mentioned for your actions are invalid unless you obtain permission from an authorized person.