Help identifying past plumbing - was it a vent pipe?

We just ripped into the leaky, disfunctional basement bathroom. It sits on a concrete slab, the far wall from the door is the exterior block wall, and the left wall from the door is the block wall between the finished and unfinished parts of the basement. The sink and toilet are against this block wall.

What we discovered is that, after the P trap, the sink drain goes straight through the block wall, comes out 3" from the wall into the unfinished basemet, hits a T joint, and then goes straight down into the concrete slab. The T joint is oriented so that the 3rd branch points straight up, but there is nothing connected.

I figured on three possibilities:
1) The plumber ran out of elbows and used a T joint.
2) There used to be a drain plumbed from the 2nd floor which ran through that T joint.
3) It used to be a vent pipe.

So, since I didn't see one elsewhere, I guessed vent pipe. The tub and the toilet each have one, but the sink doesn't. Let me know if I guessed. wrong.

But really, what do I do now? The main stack is about 6 feet away (but I don't know where or how this sink connects to it, under the concrete) - can I assume that the sink may be "wet vented", so just cap the T joint? Or should I connect a vent to the sink?

If I need to vent the sink, does the pipe need to be at a continuous rise, or could I, say, run it at a slope to reach the exterior wall (somewhere between 30 and 45 degrees), or even straight up, then horizontal along the ceiling? Is PVC okay?

from what you described it sounds like an in the wall vent, except in your case it couldn't go into the block wall. If this is a in the wall vent it should of had one of these on it.

http://www.homedepot.com/h_d1/N-5yc1v/R-100204205/h_d2/ProductDisplay?catalogId=10053&langId=-1&keyword=secondary+vent&storeId=10051&relatedSearch=secondary%20vent

Check the drainage of the sink, fill, drain, notice the flow rate. Now plug the pipe that is suppose to be the vent and retest.?

I think your guess was right... I'm too familiar with pipes.

I saw a similar pipe in my basement and left it alone although it seemed out of place. Thank you ron45 for your link. I think that in line cheater vent could work. I will be doing some renovation in my basement after I moved all the items out as I want to use the basement as an entertainment room and not as a storage facility. I just discovered the pipe and thought it would be good to do some research before getting the contractors in case they decide to pull a fast one. I am currently busy moving all the stuff to a self storage here in Sydney but I would like to ask if anyone knows if redo the plumbing is a good idea as the plumbing in my basement is really really old.

If the plumbing will be hidden, replace it with new.

If you are installing a bathroom in the basement and don't have the plumbing ran yet, here is an easy solution.

http://www.homeclick.com/saniflo-saniplus-elwh-saniplus-two-piece-elongated-toilet-with-macerating-pump-in-white/p-174168.aspx