The HP-2 does not have a Alkaline switch in the battery compartment. It will charge when it is on but only with a 1000 mAh Smartphone plug it is supposed to prompt you to charge but of course mine does not charge at all. I've never even seen the charge light come on before.
Yep, that's all correct! I'd just dug up the manual.
The manual almost makes it sound like it will still prompt you to select DC power even when using a smaller power source and then goes on to say that it will not actually start charging with the smaller power source until you turn it off.
I've seen plenty of bad cables in my days as well as power bricks.
If your cable is good, you should be able to get the power prompt by plugging the cable into a USB port on your computer. If that test works, the power brick is faulty but my bet is a faulty cable if it's not a physical problem with the scanner.
If you have another cable laying around, try it by plugging it into a live computer USB port and see if you get a prompt.
That's the only way you will get your answer.