No it's delayed because of the digital box. I removed the box in my office and compared it to the room without the box and it's a few seconds quicker. If you connect the cable directly to the TV it cuts out the delay. CNBC is so far behind anyways a few seconds isn't going to make a difference. They are just slow.
I have no idea what is going on with your setup but what you are saying does not make sense unless by connecting the coax directly to the TV you are viewing an analog version of a channel and the digital version of the same channel is being lagged before it gets to you. If you are watching the same digital channel then you arent going to see a difference between tuning the channel with your TV's digital tuner vs tuning it with a digital cable box. A digital cable box cannot add seconds of delay - that would require massive amounts of buffering, e.g. a DVR-type box.