1998 Buick Century water soaked carpet under glovebox after

mamabula....I have a '99 Century 6 Cyl. and had the same problem.
On passenger side, bottom of windshield where black plastic meets glass, if you take that black plastic cover off (pulls straight up and off) there is a piece that is normally glued to the bottom of the windshield...it diverts the water to the extreme right side and out a hole to the right front fender onto the ground. It's a small U-piece that I siliconed back onto glass and also siliconed the black plastic piece when reinstalling it...
Unfortunately, I had to pick up the carpet and let it dry for a few days - some say use a heater or hair dryer but I just let it air out for about three days...the water actually runs down the inside firewall under the carpet and just soaks thru.
Not sure if that piece is your problem but hope this helps...Wallboy