Without digging around a bit, my first guess would be that the water is coming in through the door seals. I'll bet you will find cracks in the plastic trim that serves as a "gutter" for water coming off of the roof. These cracks will probably be right where the screws are. That's part of the door seal problem. The other part is that there is no sealant between the gutter and the body. Ususally there is butyl rubber that helps secure the rubber door seals but does a poor job of preventing water from entering the channel. Lastly, you'll probably find that your door seals shrunk. At the bottom of the door opening in the center of the sill is where the seam is. It's under the trim so you might have to pull it up a bit to see it. If the seam butts right up then check the area at the top corner of the seat back where the door opening makes the sharp curve. You may find that the door seal is not even on the body at that point.
On my 93, I added this stuff called Strip Caulk. It's purpose is to seal gaps in residential windows and doors. It's a non-hardening sealer so you can remove and reapply if necessary. The problem is that it's redish-brown in color instead of black. Since applying this, I talked to a buddy of mine that owns an auto glass shop. He gave me a box of 3M Ribbon Sealant. This is the stuff to use:
The sealant should be applied to the gutter trim on the back in between the yellow and red lines: