I had major windscreen seal failure in my 2011 S40. They are from the same era, so you may have teh same problem. The glue simply let go.
Here is what you should do:
1. get a condensed air can or a vacuum cleaner that can blow air
2. get some soapy water
3. apply the soapy water around the seals
4. blow air at the seals from inside the car
If you see bubbleing, you will know which seal has failed. If it is the rear windscreen, do not attempty and home repair, bring it to a shop and have it replaced.
If it is the doors, you can try to bend them back in place (gently).
The water is probably flowing down below the trim, which is why you don't see it.
Be careful of mold. Clean it carefully if you see any (don't breathe that stuff in).
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