If you have and know how to use a DC ammeter, check current draw with all accessories turned off. If it's more than the milliamps normally drawn by stereo or other electronic memory features, start pulling fuses until the current draw lowers noticeably. Could be something as simple as the trunk or under hood light switches fail and that light can stay on, out of sight, out of mind, or it could be an unintended ground, or faulty electronic device that can be tricky to isolate. Good luck.
Is this checked by removing the ground cable and testing between the terminal and battery post?
I vaguely remember doing this with a test light back in my jalopy driving days.
Any reason not to use a deadman switch and cut power to the battery when the car isn't in use, I mean other than resetting the clock and pre-sets on your radio? Might be cheaper/easier than trying to diagnose the actual issue.
EDIT-----
Just re-read the OP and realized it died while he was driving, rules out parasitic draw unless there was a good deal of time between when the battery was replaced and when this happened (time enough to build up sulfates to the point that the battery won't take a charge).
If the battery is new, check the cables for corrosion. When the car is running, make sure the alternator is putting out > 14v (check at the battery terminals).
Not to belabor the point, but you are saying when you read across the battery terminals, you are not seeing that 14v? Should be easy to track back then. Usually not a lot between the alt and the battery. I think the first thing to look at is the ground cable from the battery to the chassis.
Good video.Not to change the subject but.
I have an older vehicle to when sits over a few days the battery is dead.
Took the battery in for load test and they said it was good.
Alternator voltage checks good.
Now I am try to diagnose for key off battery drain.
I found this: http://www.aa1car.com/library/battery_runs_down.htm
Will try it this weekend, but any other good checks?
Edit:
And prior to this happening I smelled something burning and noticed the radio doesn't work.
But I was thinking when something burns up it would create an open. I can check that by pulling the fuse.
Where in the Hell is Aps when you need him!?!?
Did you wind it up enough?
That's what my brother used to ask about my Subaru BRAT.