Triage
There is a lot to be learned from triage. Anytime you enter into a situation that requires a great deal of problem-solving/fixing, I like to recommend you treat it like a triage situation.
The first order is to prioritize the problems. What requires immediate attention? What is deadline prohibited that cannot be altered and is necessary to the well-being of the department/organization? Next, what are short-term and long-term issues/solutions? And so forth.
I always tell senior management that my first priority is to stop the bleeding. Stop that which is likely to lead to the death of the patient (department/organization). Once that is accomplished, then we can go about fixing the problems one by one in a well-defined order while keeping an eye on possible side effects or new conditions that could possibly arise (new threats, change of personnel, etc). Next, rehab the patient (department/organization). Get them back on their feet. Slowly, but surely, get them moving again and being productive. Last, go full speed ahead. Explore new opportunities and take on new challenges.
Too often managers are looking for the "big win" and realign the order of triage. They fail to stop the bleeding and instead focus too much on new opportunities and new challenges. They may indeed present themselves, but if your department/organization is not prepared to handle them, you only exacerbate the situation and your patient (department/organization) dies.
Lastly, with each problem rectified, ensure that there are processes and/or solutions in place to ensure that the problem in question doesn't surface again. In other words, do it right. Don't do a half-ass job only to have to go in and do it all over again. Put the department/organization back on solid ground, not quicksand.