I have a wide PVC pipe coming down from the roof in the attic. It goes horizontal across the depth of the house on the floor of the attic, but before it does that, there is a branch off to a smaller pipe. There is a leak at that joint, which is odd because it makes me think that the big pipe is blocked, otherwise why would this area leak. See attached. I probably cannot fix this myself, however I am just trying to analyze how big of an issue I am dealing with.
Thanks!

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Odd place for a leak. Since it's a vent pipe any water entering from the top would go past that joint towards the lower elbow.

One of the pro plumbers should be along, but my guess is that you will be able to fix it as it is not a pressurized pipe and if you have roof access it can be snaked if there is a clog.

 

Could it be a dead animal blocking the pipe below the branch off?

 

This is something you can try to fix yourself. Assuming the leak is where you indicate in the photo (not leaking at a higher joint and exiting where you indicate the leak) do the following. Clean the joint area with lacquer thinner or acetone. Spread silicone caulk around the joint. That should do it. The vent pipe is at atmospheric pressure so the silicon caulk should dry in place. A good check would be to place a pan under the repair and check it for water after a couple of days. The water is coming from the moist vented air where the moisture is condensing on the cold vent pipe. Good luck

 

Look up with the lights off in the attic during the day to see if you can see day light coming in around the vent seal on the roof.
I'd clean and use PVC cement not silicone.
Got some issues going one with the way that insulation was installed.
#1, Pull some back and see if they took the time to air seal around and plumbing, wiring, and ceiling fixtures.
#2, Insulation should have only been as thick as the height of the joist, need more then you run unfaced over what's there in the other direction.
Really would have been far better off with blown in.
I would think if the drain was plugged up enough on the inside to leak there you would not be able to flush a toilet or drain a sink.
If it was condensation all the pipes would be damp, check with a piece of toilet paper.
Condensation may be from a lack of roof venting, soffets covered over with insulation, attic not air sealed.

 

Take a small level and check to be sure the problem branch is sloped down away from the larger vent pipe. The coupling at the leak is feeding up, so any condensation inside the branch needs to drain away from the larger vent.

In any case, there should NOT have been a leak. I'm not a plumbing pro, but I believe they make a two piece ring that can be glued and pushed up against the leak point. Years ago I used to use a coupling, cut a 1/2" and ring and split the ring as needed to fit over the pipe. The pros will have a code compliant solution.

Bud