So first of all, at this point, I do not have the specs on my furnace. The furnace is located in a small closet raised slightly over the vent that sucks in the air from the house. The closet is located in the upstairs hallway. It is really hard to view along the sides of it, and I can not even see the rear side. Anyway, I noticed that the open space behind the air filter was all damp from a leak, so I killed my AC (house is 90 degrees!). I did some inspection work, and there is a copper pipe (that is cold to the touch when running) runs up above the furnace and into some sort of rectangular duct that stretches up into the ceiling. Water is leaking from where the pipe enters this duct. It drips off the pipe, and leaks all the way down the furnace, moistening the furnace support wood, and then lower into the open area where the air filter is. Does anyone have any ideas? Right in the middle of a 100+ degree heat wave!
If the copper pipe is bare, it should be insulated. Condensation will form on the cool pipe and drip down the unit. You can get foam insulation at Home Depot. Wrap the pipe with the insulation and hold in place with duct tape. If this is not the case, then your condensation drain for the a-frame is clogged. You will have to unclog it. I have used a shop vac and actually sucked out the blockage. You can also use the pressure from the garden hose. This can get messy. The clog is not solid. It is the gunk that has built up in the drain. The vacuum should suck it out. When you do get it open,,,pour some bleach in the drain once a month to keep this from happening again.
You have a few different things going on - water not draining, no air-flow and no cooling. Water and reduced humidity are the result of moisture being taken out of the air. The ducting section just above the furnace is where the A-coil sits and it is normal for it to generate lots of condensation water as it takes moisture out of the air flowing over it. Normally, this water collects in a drain pan inside the unit under the A-coil and is drained out by a PVC pipe that runs out the front or back of the unit and into an open basement drain. Often this PVC pipe gets clogged with dirt and then the water will have nowhere to go but come out through the ducting or into the furnace below. I would start with cleaning out the A-coil and the PVC drain line. There are a few screws holding an access panel in the ducting above the furnace and if you remove them, the access panel should come out and give you access to the drain pan. You should clean the pan and the PVC connection to it to the point where water poured into the drain pan it flows freely into the basement drain. While you have the access panel open, use a small mirror to see if the A-coil is clean and you can see through the fins with a flashlight. If you cannot, then you need to clean the A-coil as noted in other answers here. That should fix the air flow and the water issue. I would next clean the outdoor unit coil (make sure the outdoor disconnect is pulled out). If everything is clean, both fans and compressor run and there is warm air, I suspect a low refrigerant issue that will need a call to a tech to diagnose and correct.
It is likely the return line, the larger one, for your refrigerant going back to the compresser that is dripping. In the simplest terms it is simply still too cold after leaving the coils in the furnace. Yes, you can try insulating it, but for the most part that is only treating the symptom, not the cause and will only push where you get the condensation to further down the line in the ducts. But the moving air in the ducts should be drier. So how do you make it warmer? You need more heat exchange and that means better air flow. Most commonly your coil in the furnace is getting dirty, plugged with lint. That reduces air and insulates the coil and reduces heat exchange. Other than that you need to move more air. Don't use a filter too restrictive, make sure all your vents are open, and the blower wheel is clean. If you haven't had the coil and the blower wheel cleaned in a few years, or never, then that is the first thing that needs doing. Beyond that there are some sealed system issues that cause it, like overcharging, an oversized compressor, a bad or oversized expansion value and the like. But those repairs are costly. But if those were the problem it would have been doing it from day one. Start by getting the coil and blower wheel cleaned well and hopefully that will take care of it. Good Luck.