First things first; you were only offered a Trade-In value because you were tring to buy a different vehicle, correct? If that's not the case, you should ask for retail instead of trade-in.
In the case when you trade in a car that is worth less than the amount of the note, then you are "upside down." Happens all the time, so don't worry. Now, to answer your question, when you're upside down on your vehicle and trade it in for a new/different one, the amount of negative equity (in your case $4,200) gets transferred over and becomes part of your new loan. When that transaction occurs, the dealerships owns your trade (your KIA) and you don't owe anything on it, but you also no longer own it. So let's say you bought a new car and it cost you $15,000 and you have decided to finance the whole thing, now because of your "upsidedown'ness" you are actually financing $19,200 (the $15,000 for the new car and the $4,200 that carried over from your KIA). It might be hard to get a loan for that amount but it can be done.
Let me know if you're still confused :)