It's not your job to hack into your network on your 1st day. Especially if you're the IT manager, plus if you're the manager I'm assuming you have a systems admin or two that can help you with this problem. Otherwise lose the IT manager handle and just call yourself a PC LAN Technician (I can almost hear the frantic shouting in your original post, "Oh No, what do I do?")
Speak to your boss & HR and have them contact the previous IT mgr, they can formally request this info which should have been left with mgmt before he left. Mgmt is usually pretty slack on this issue as I've seen this happen before not just where I work but in other places too. It shouldn't be a problem for the previous mgr to give this info. Once he provides it and you have access to the systems again, change all the required passwords (something we do where I work whenever a system admin leaves the company).
If they can't get this info from him willingly then they can pursue some form of legal action against him at which point you'll be forced to use some 3rd party vendor tool like Winternal's ERD tool suite or resort to some linux bootdisks which allow you to reset admin passwords and what not (I'm not advocating hacking just saying that there are resources available if the situation calls for it) - this isn't an impossible situation.
If the systems are still running and no one's complaining about system issues (ie. user's can't print, IM or email's down, can't access network shares on the file server, internet access is down, etc.) then don't fly off the handle, you seem to be running around like a chicken with it's head cut off.
Don't sweat it if you just stepped into this shop and don't have the info provided to you, it can hardly be viewed as your fault or you inability to fix a problem. Just act like a manager and manage the situation professionally.
Just my 0.02 cents cdn, feel free to agree/disagree.