It sounds like you're removing the headcap/bezel. Is the LED out in the open when you take the head off? The section just below the headcap turns for changing modes.
edit; when you completely unscrew the section that changes modes, the battery will be able to come out that end.
Well damn. Just got to my parents house to upload the photo I took and then I saw this. I feel dumb now, I had a feeling I might once we figured out what I was doing wrong. I've been turning the head bezel, which is why I was confused. I didn't even know the body could turn where you described. Problem solved, thank you very much, and thank you to everyone else for being patient with a newbie to flashlights.
Curious, I'm using an energizer lithium battery BTW, non-rechargeable.
I'm off to some woods for a bit to play with my now fully functioning light.