Included video is here: https://www.youtube.com/watch?v=iorvSoMjvaA&feature=youtu.be
The reason for pausing to start is for the glow plugs (diesel van).
Battery is OK! I tested myself and at an auto parts store. No problems at all with the battery.
Description: When turning the key, I can hear a click from the engine bay (I believe this is the solenoid, but the starter motor either does not engage, or just barely turns the motor over).
This is an intermittent problem! It first occurred over a month ago. It can go weeks without having any problem, then it happens all the time.
The trick I used to finally get it to start: I turned the key 90% to full, then released to 30% of turn, an turned back to 100%. This "double-turn-without-release" trick, whatever it does, seems to usually be successful in starting the car--I have no idea why, though!
Edit: I forgot to mention this: The problem seems to occur only on the first attempt to start the car for the day. After I've got it started and everything warmed up, starting it again has had a higher success rate. It is still intermittent, though, sometimes it still shows this problem when warm, but the likelihood appears to be much less.
Second edit: Tested starting the motor with a voltmeter. The starter motor is getting 12volts on successful starts, but getting less than that when it is not starting.