It's been reported that after applying January 2016 update (KB 3114506), customers are experiencing an error on Windows Server 2012 R2 and Windows Server 2008 R2 when trying to launch Office applications such as Excel, Word, PowerPoint and OneDrive for Business.
System Error - The program can’t start because davclnt.dll is missing from your computer. Try reinstalling the program to fix this problem.
Sorry, something went wrong when trying to obtain a shared computer license for Word. Error code: 0xc004f014
Excel application error:
Word application error:
Currently, Microsoft is working on the issue and will be providing an update when a fix becomes available. As a workaround, install Desktop User Experience, which ensures the davclnt is available.
See this article for further information:
Error: The Program can’t start because davclnt.dll is missing from your computer
This issue was fixed with KB3114736, February 2016 update.
3114736 February 9, 2016, update for Office 2013 (KB3114736)