So you decided to determine why water is on your floorboards carpet..
UPDATE: see this post here also now. [link]
"Wiper Remover 2005 Chevy Cobalt, cover, water deflector, floor carpet wet leaking fix"
"Wiper Remover 2005 Chevy Cobalt, cover, water deflector, floor carpet wet leaking fix"
So there is water on both the left and right side on the driver foot well and the passenger side but it is in the middle on the left closest to the center console as if the center console is leaking on the passenger side.
[Updated photos from the post referenced at the start of this post. This is where the rain water leak came from a deteriorated plastic cover over the glovebox air filter, causing water to leak on to the carpet.]
I put RTV on at the top. Comes with a glue ring already, just press to install.
see newer post for removal. the water line to the wipers can be left alone.
I either have a air condition backup causing a leak from what I researched or water is leaking due to debris in the bottom of the windshield, or some other thing like the windshield is leaking.
I have no idea? 
There is video and posts about a compartment in the engine bay up against the firewall basically looking into the engine bay on the passenger side that can get filled with debris.
The Internet Research:
1.) Take it to dealer and have them blow out your HVAC (A/C) drain line.
His was clogged and was causing water to drain into the passenger compartment and blowing it out solved the problem.
2.) But even if the AC drain is plugged, it should be wet every day he had the AC on, not just when it is sitting out in the rain, right?
3.) Speaker pull the door panel off. Apparently water can enter via the speaker hole?
4.) The AC condensation drain tube is inadequate it will run back and down onto the floorboard. Fixed it with a 90 Degree fitting on the drain tube to ensure proper drainage outside of the vehicle and it has been fine for a year. (relative to the 2000 Mitsubishi Galant, not cobalt)
5.) Water leak test the windshield. Carpet should be removed and dried out, replace matting if necessary, because it will never dry. Look by front firewall floor for drippage. Windshield moldings must be removed if resealing is necessary, and be sure to use a neoprene water resistant windshield sealer. (not sure what vehicle?) I can confirm water on floor doesn't dry after a week or two unless mine is getting wet again and again.
6.) The drains in the wiper wells are probably clogged. You need to remove the plastic 'vent screen' under the wipers to clear out debris. Remove the wipers and a few screws, not difficult at all. Also under the hood, you will see a vertical tube on each side of the car under the wiper wells. These can be removed from under the hood without removing the wipers, but you will probably have to clear the wells anyway. What happens is the water backs up and enters the car through the fresh air inlet and comes in around the blower fan. (not sure what vehicle?)