[fjtorres]

Not sure about the plus, but on the original 360 the reset button and the battery reside under a panel that slides out in the rear.
If you look at the rear of the reader, the bottom half slides out under firm steady pressure. You can help it it by carefully running a finger nail along the barely-noticeable gap there. Don't rush it, force it, or lift it; just slide it out. The first time will be the hardest because it s a nice, tight fit.
The issue isn't the battery but that you need to reset the reader.
In unplugging without ejecting, the reader looks like it might be locked up.
Think of a locked-up laptop; first you try the three-finger salute to reset, if that fails you unplug and remove the battery, and in the worst case you have to reinstall/reimage the system. Same here.
Odds are the reset switch is all you need.
Just remove the sd card first in case its file system got corrupted and needs reformatting.
If the system resets to normal without the card, power down and then try with the card.