Rain getting in my S14!!

[CreAziaN]

On the windshield, there are some mouldings located right beneath the windshield wipers. They're really loose right now and could probably be ripped off without much force. I suspect that these rubber moulding strips are what is allowing water to leak into the car. After a storm, you see a puddle of water undernearth the steering wheel on the floor mats.

Do you think the mouldings are the problem? If so, how hard/expensive of a fix do you think this is?
Do you think the rain will make the car start to smell after a while?

PS. This is a '97

[Al_S14]

Do you have a sunroof? if so i am 99% sure your drain is cloged up. to clean them you need to remove the fender liner and blow compressed air in to the drain(make sure the roof is open). If you dont have it sorry i am clueless without looking at it

[CreAziaN]

No sunroof...It's getting in thru the firewall/windshield or something. I'm thinking firewall because that's how it ends up on the floor mats.

[projectRDM]

Doubtful. The lower trim on the back of the cowl panel just keeps the plastic from resting directly on the glass, it doesn't seal anything. Mine has been gone for the longest time with no ill effects.
Below the cowl is where the wiper mechanism resides, it's a completely sealed bulkhead area with drains on either end to allow water to flow out behind the fenders, the only opening anywhere in it is the fresh air inlet for the blower motor and it's covered by a plate so that water can't directly access it. Your intrusion is coming from somewhere else unless that plate is missing, again which is doubtful.