My advise is to get yourself a good performance monitoring tools e.g from Quest, Red Gate, Idera etc that will definitely save your a$$ as a non DBA. You'll notice the problem of your problem from the tools.

I think your previous DBAs had done some query to reindex or defrag the indexes on interval. That's why you found slow reporting services in your company after they left. try looking for that script jobs. Or maybe, you need to refresh the server by restarting it. Look for the DBA's log books.