Pontiac: a/c leak passenger side floorboard, pontiac grand prix, vent hose

Question
1997 Pontiac Grand Prix GT 3.8

When I run the AC on my 97 Grand Prix, I'm getting a water leak in the car. Actually, when I turn LEFT and the AC has been on for a while, you can hear water 'rushing' from one side to the other in the front under the dash. At least that's what it sounds like. The first thing I did was find the rubber piece attached into the firewall from underneath the car.  I pulled it off and stuck a tool in there to try and loosen up any gunk possibly clogging the drainage.  A few drips of water came out, but no debris.  Then, I took the glove box out, and noticed that a rubber tube that goes from this silver cylinder (3 in. diameter - not sure what this part is called) that sits just below the blower, was wet and that the hole in the middle of the silver cylinder was a bit wet, too.  There is a tube going from the side of the cylinder facing the firewall, into the firewall ( I assume this is connecting to the tube I tried cleaning out from underneath the car). Anyway, where this tube connects into the silver cylinder, there is moisture and a slight drip.  I think this may be my issue, but over to the left of this housing is a plastic box that had some condensation on it, but not a drip.  Not sure if I should get a new one of these tubes.  Not sure what it is even called.  Your thoughts would be appreciated. Thank you.

I have no idea where to go from here

Answer
The silver cylinder is your blower motor. The tube that attaches to it is a vent hose that directs air flow to the motor windings to keep them cool so that the motor wont burn up.
The drain tube is the one outside that you tried to clean out. If the drain is open and you are getting water inside the car, then there is a leak in the HVAC case. Look for missing screws or gaps in the seams of the case.