Going from 2008 to 2016 is jumping too far.
I suggest you to go move to 2012 first and then to 2016.
First of all download Microsoft Migration Assistant and try to spot incompatibilities.
Then download Microsoft Assessment and Planning Toolkit and scan for all sort of incompatibilities following a guide.
Spot the incompatible queries using the Query Tuning ...
If you don't find anything in the logs (it could have been taken OFFLINE a while ago) you can always check the date modified of the physical data files of the database as it would have not changed after been taken OFFLINE.