So you have a multimeter and the skills to replace a starter so we are in good shape. Do not bother doing resistance tests as if you have one good strand in the wire it will show good numbers and you will just be on a wild goose chase although a bad reading would be an immediate sign of problems just don't let a good reading fool you. Couple of tests that should be performed would be voltage drop tests across power and ground. You will need an assistant for this. So you will place your voltmeter on DC voltage. Place one lead on the negative battery post and the other lead on a clean spot on the engine block as close to the starter as you can get, if you pull up the air filter box the top starter bolt will be a good spot, have your assistant try to crank the engine which will put a load on the circuit and see if you see voltage, anything in the 0.2 volts or more range implies resistance in the ground circuit although a good battery would likely overcome that small but you see anything over that it is a sign of a bad ground. Do the next test, place your lead on the positive large wire from the battery to the starter right on the post, the other lead will need to be attached to the battery post itself so this one will be tough if you don't have a lot of accessories for your meter, same thing you will be looking for, when you try to crank by loading up the circuit you should see next to no voltage in that circuit, you see anything over 0.5 volts on the positive side and there is too much resistance in that circuit. You can also start by checking the voltage drop right at the battery terminal to see if they are bad, put one lead on top of post and one on the outside of the terminal and voltage there while trying to crank is the result of a bad terminal. Of course one other issue could be the clipped in signal wire, I assume you don't have a pin tension gauge to check it so it is dangerous for me to recommend this but if you take lots of precautions with a trusted assistant you can have him/her try to crank it while you wiggle the signal wire on the starter, if your assistant runs you over or you get your hand trapped remember I said to be smart about this. One of those is likely to be your problem if you are certain you have a good battery and that your positive post is tight on that battery (if I only had a $ for every Auto zone battery that the posts are too small for the kias and cause this problem)