It's unlikely it's a bad joint. Even a dry-fitted vent run probably won't leak; there isn't enough pressure or volume of water in there (even in a storm). My guess is the leak is coming from the flashing around the vent pipe exit in the roof - not from a defective coupling. The water might be running down the outside of the pipe and dripping off the el. Can you gingerly use a ladder or an extension pole and rag to detect moisture on the underside of the hole?
If the problem is the flashing, then you need to fix it from the roof (read, HAVE A PRO DO IT; DON'T GO SHEMANGLING UP ON THE ROOF YRSELF). If you just caulk the underside of the exit hole attc-side, then water can enter the roof sheathing from above and potentially rot yr roof.
If the problem is a leaky el, then the right thing is to cut it out and replace it. However, if it were me, I'd first caulk the seams of the el. and see how that holds up. Since there's no pressure in the vent pipe, caulk (silicone) will probably suffice.