The thread under title "The Microsoft Office cache encountered a problem (with Office 2013 ProPlus Preview/Beta)" described exactly my problem, but discussion on that thread has been locked without any solution to the problem.
I'd like to add one symptom to this case. All problems started when I installed SkyDrive Pro in order to access my Office 365 files on a sharepoint site of mine. Without Lync program, I managed to run both SkyDrive and SkyDrive Pro simulteneously for short
period of time, but installing Lync (or any other "disturbing" of Office) makes this Document Cache fail over and over again.
At some point of a boot procedure, apparently while putting up this SkyDrive Pro, system gives an error message upon file in use preventing synchronization. File is allegedly in use with other process that is suggested to be closed. Problem is that there is no apparent program using that file. File in question is the very first file within the group of files I've stored in the sharepoint site in question. It is always the very first file stored there.
I would very much like some advice about how to get these local Office 2013 installation and Office 365 P1 -system work.