Sounds like a plugged HVAC drain.

 

Hi I had the same experience with my 97 Blazer. I had a puddle on my passenger side after 3 days of constants rain. I had worn door pins and bushings as well. I bought a new door gasket kit for both front doors although the originals didn't look that bad I thought they might be misshaped from the sagging front doors. Well I put them in and I still had a slow low volume leak when I soaked with a garden hose. Main leak area was around where the gasket runs by the dash and downward. When I looked the gasket would collapse or develop a crease in it small enough to let the water run through. Because the gaskets were new and seemed normal I wasn't too happy. I fixed the problem by adding a little reinforcement for the gasketing to prevent it from creasing/collapsing. I used some 1/4" foam tubing (used for stuffing in cracks around windows etc. for home renovations) and some doublesided tape (1/2" wide). I gently moved the large round circular part of the gasket in the direction of the rear of the vehicle and laid in the tape and the foam tubing. (right in tight against the backside fo the big circular part)
I then ran my finger the length of the tubing to ensure a good stick and then gently pressed back the gasketing into normal position and help keep the foam tubing in place.
I reinforced this way in two areas on each side. I did about 10" length each to ensure that it was long enough for sufficient grip over a longer area to prevent future dry out and fall out.
I did this last summer and the vehicle has been through +90 to -40 temps, rain and snow and it's been perfectly dry.
After a week or two of the repair it was interesting to notice a stronger leather smell from the interior versus a slight musty damp smell that wasn't initially apparent.
This might be compensating for other imperfections but the doors are not loose or sagging and it was the most effective fix.
Since it worked me - if the foam tubing starts coming loose in the future I will apply a thin bead of silicon instead of the double sided tape for a permanent fix.
This might be worth a try if you can pin point the leak as I did. (I had to observe several times to nail it down)