Leadership, communication and motivation in the criminal justice admin

I have been given a scenerio dealing with criminal justice administration and I need some guidance.The situation is, I have just been appointed as the new court administrator for a medium sized court system with approximately 75 employees and five full time courts. This is a new position for the courts, as in the past each individual court has primarily managed itself, except for the employee hiring process, which was completed through the County Human Resource Division. Upon taking my post Iquickly find out that none of the courts seem to be willing to cooperate with each other, or for that matter, any of the other various county offices, such as the County Clerks Office and the District Attorney's Office. Rumors and gossip about mismanagement abound, and the communications process between the five courts appears to be at a stand still. The courts currently have a huge backlog of cases awaiting trial, and in addition, employee morale is low and the turnover rate high.

I need to know how I would go about responding to this organizational problem.

Which problem would you address first, and exactly how would you address it?
In addition, how would you respond to the employee morale and the turnover problem that was identified?

What techniques could be employed to improve communications throughout the organization and create a more harmonious work environment?

What method or tactic would you use in order to reduce the backlog of cases awaiting trial?