I think you answered your question on your own: "I specify that all the PCs in the box are in the same case except one, we have a common MASTER settings file. The PC that works has not loaded this master!"
Make a backup of the settings of the working workstation and load it on the other workstations.
An SLDREG file can be corrupted a few times. It happened to me once when, after reloading the SLDREG, it prevented me from opening SolidWorks!! A shame all the same!
The problem is that we need this master file, it manages all our basemaps, all the colors, links to the server etc ... so that everyone has the same basis for work.
The PC that doesn't have the bug has none of that (is blank) so if you reload its settings in all the PCs in the box it's going to become anarchy.
I've often been told (even though I've never followed this advice!) that you have to redo the SLDREG entirely every time SW is changed. Wouldn't you have recently switched to SW 2014?
But this is the first year that we are implementing this, so no hindsight on the 2012 version of SLDW.
I think that in the end we will use the PC that does not have the master to "decompress" the STEP and IGES and save them correctly in SLDW. We will be able to resume studies with all our other PCs: it will not solve our problem but while waiting to look at the sldreg code it will help out!