Water coming out the floor vents

Been battling a puzzling problem for awhile now.
When I purchased my wagon it had been garage kept since new, but now that it is regularly outside I have been finding leaks.
Most recently I backed out of my driveway (slight incline) after a rain and water started streaming out of the floor vents.
I repaired one recently where one of the cables goes into the heater box, which was dried out sealant, but this has me stumped.
It's my '87 Caprice, non A/C car.
I noticed the bottom of the windshield glass is delaminating slightly, but I don't know if that is related.
Any ideas would be greatly appreciated.