Both the 2D and 3D caches are kept in the user temp folder. So for example, on a machine where this hasn't been modified, and I'm logged in, it is C:\Users\mbranscomb\AppData\Local\Temp\E3.
Unfortunately at this point I cannot think of a reason why the service would simply not display in 3D but does in 2D. You could try creating the Explorer log folder and take a look at the contents of the log file e.g. C:\Users\mbranscomb\Documents\E3Log. Remember to delete this folder though after you've done your research - a lot of information gets logged here so the file could grow rapidly and it may slow down Explorer slightly. You'll see the line like "14:13:43 - 3780 - MapDisplay::DisplayMode::set Display3D" when you try to switch to 3D.