Alternator smoking??
 

My 2003 MDX had been sitting for a couple of months and wouldn't turn over after a 20 minute jump. So I replaced the battery. Still wouldn't start but got some noise. I did a long jump and it almost turned over. I tried a few times more but then I saw some whitish smoke rising out of the from of the engine. I couldn't quite locate the location. Is the most likely cause the alternator? Also -- if I buy a used alternator what's the latest year of this gen? Thanks in advance!

Your 1G MDX was produced from 2001-2006. I am not sure of specific changes in the alternator within the model years, but they are usually pretty generic.

If it's smoking, it may be either a short in the alternator or the bearings inside are worn causing excessive heat and friction. This usually causes a belt squeal, but there's a first for everything.

The water pump went out on my RDX by making a tapping noise, but no belt squeals or leaks, go figure?

Yeah, it's probably the bearings, go ahead and replace it!

If you have a 2nd, known good battery: Disconnect both the red and the black cables, from the suspect battery.
Connect the cables to the known good battery and try to start the car.

Some batteries will develop an internal open and appear to hold a charge, until placed under a load.

Yeah. Tap the starter a few times and if she's dead you have a bad cell in the battery and it's been starting on surface charge. Older Toyota's do this to their batteries all of the time.

I turned the old battery in when I got the new one. It was 5 years old anyway.