Is it permissible to use an illicit patch to activate a computer protection program in order to protect private family photos and videos from being hacked, in the event that one is unable to purchase the original program or find a free version that provides the required protection?

What you mentioned is not a necessity that permits infringing upon the ownership of the company that manufactured the program. Intellectual property rights must be respected, and it is not permissible to violate them. You must purchase the original program or seek another way to protect what you fear might be hacked.