I have an 18v dewalt cordless drill which I used regularly. In the middle of a project, I put in a newly charged battery and it immediately started to smoke from the battery case. I assumed that it was due to a bad battery, so I removed it quickly and popped in another battery which did the exact same thing. I did take it apart to check for moisture and everything looked normal. I did not remove the brushes however. Is this the drill or possibly bad batteries?

Check continuity across two pins on drill that get power from battery. If they are 'touching' or have continuity the drill is bad. It sounds like that is the case as two batteries did the same thing. Can you try the batteries in any other 18v dewalt tool? Borrow a friends if you don't have any other tools but see if batteries do the same.
Also, measure power of battery before you put it in and see how much the afterward you had it in for a second how much power it has. If it is shorted in the drill it will drain power. Sounds like a short inside drill. GL