The thieves must have had access to your fathers passport or cedula, how did this happen?
Tell the whole story, what you wrote is neither here nor there!
I'm surprised the police were interested in something like this for a week, unless someone was killed that was a friend, family member or work colleague.
Strange situation, I'd even hazard a guess they weren't even cops. Don't tell me! landed on your door and didn't actually take you to the police station at all. Showed you an old ID, yes maybe of them. Told you they could make this go away if you paid them, and allowed you to make the offer of how much. Am I close? Loads of police who have been fired over recent years for corruption still carry their old ID and make a living threatening to lock up gringos and scarring the hell out of them with the threat of jail.
Am I close?