The speedometer on my 1999 Kia Sephia is not working.?

A couple of weeks ago I was driving my 1999 Sephia and noticed that the speedometer dropped to 0mph for a second but then immediately went back up, so I didn't think much of it. A couple days later I tried driving it in the morning and the speedometer wasn't working at all, it was continuously stuck on 0pmh. For a while the speedometer was the only problem, but then it started running oddly- driving slowly as I pushed on the gas and then speeding up suddenly (I don't know much about cars so I'm not exactly sure of the technical description of waht it was doing). At one point it stopped doing this, and simply would not speed up at all...took me about 30 full seconds to get from one parking spot to the one right across from it. We have replaced the vehicle speed sensor and cleaned off/put dielectric grease on all of the electrical grounds (thinking it may have been a voltage problem), but the thing still does not work fully, as it constantly drops to 0mph when decelerating, or even just randomly drops. The car is not running "right" either, it gets very shaky when idling and still does that odd sudden-speed thing I mentioned. We plugged it into the an Actron code detector and it came up with codes regarding the speed sensor and the fourth gear ratio, but having tried several things to fix it I'm not sure what to do. Any idea if these problems are intertwined/suggestions to fix them?