OK - that would explain it.
If you're shooting JPEG (or RAW + JPEG) then the DRO does some processing in-camera so that more dynamic range is captured. For JPG shooting it is a great tool and can make a real difference to the results. The level you've suggested (Lvl3+) is a good option - although have a play with the different settings.
However, when you're shooting RAW only then you should turn DRO off. DRO has no effect on the RAW image that is stored (since DRO is only applied to in-camera JPEGs) but, and this is an important but, DRO will be applied to the image you see on preview.
The most likely visual effect is that what you see as being very dark in the RAW file as being dark/under-exposed (i.e. shadow areas) looks much brighter on the in-camera preview.
The DRO itself also has an affect on how the camera calculates the correct exposure. What you see as a correct exposure in-camera is likely to be under-exposed - which is how you described your problem - brighter on preview than on your monitor.
The best way to see it is to have a play yourself. Find a scene with quite high dynamic range (perhaps outdoors with bright skies, strong sunlight and an area in deep shadow). Set your camera up on a tripod and loop through a set of exposures as follows:
RAW only - DRO off
RAW only - Standard
RAW only - DRO Advanced Auto
etc.... (i.e. through all the DRO options)
You'll see the differences in the previews in-camera but no difference on your computer as all you will be looking at is the RAW files.
Then shoot some JPEGs with the same settings. This time when you look at them on your computer you'll begin to see the effect that DRO has.
I wouldn't for a minute criticise DRO as it's a great tool when shooting JPEG. However, for RAW shooting you should turn it off. Then you will see on your computer what you see as preview in-camera.
Hope that makes sense and helps.