Talk to management and other staff to find out what has been done in the past and what the current procedures are.
Presumably staff are still being paid, taking leave, and statutory functions are being carried out. They don't happen by magic, there has to be a process in place already.
Secondly we do not work for YOUR organisation, so we are not in position to tell you what to do or what your duties are. Every organisation is different, and more than likely, every hospital does things differently.
You are going to have to use your initiative to deal with this problem. But my suggestion is to get on top of the basics first, and keep the current hospital HR functions running. Once you are on top of that, then you can start to deal the other issues, and explore what needs improving and how you can do it.