There was a videotape of Christmas morning 1993 and 1994 so why not 1996? I have a theory that the video was erased because there was something or someone on there that the Ramseys didn't want others to see. And like you said, if the camcorder wasn't charged, then why aren't there more pictures besides just the two?
I believe that there was pictures taken of JonBenet at the White's Christmas party, but they have never been released to the media or the public.
I know we are all "Monday Morning Quarterbacks" here, but one of the things that could have been done was for LE to actually check the battery of the video camera to see if it had a dead battery as JR said it did. Between all the activities of the day, going to the White's, dropping off the gifts on the way home and staging the death of their daughter to look like a kidnapping, there shouldn't have been time to charge the camera.
I also find the lack of video/photos suspicious. This ties in with JR hiring a lawyer for his older son (JAR) and his ex-wife (JAR's mother) who lived in Georgia. JAR was alleged to be with his mother Christmas day/night, though there is no proof of that. The ex-wife was never a suspect by any means, and there was no good reason for her to have her own lawyer. To me, the only reason was to prevent her from having to be questioned about her son's presence that day/night and to provide (if possible) any photographs or videos corroborating his presence there. There was supposedly a movie ticket in his coat pocket, but not for that day. There was also a grainy ATM photo showing a young man, but there was a baseball cap down over his eyes and frankly, it is impossible to tell if it was him. In desperate circumstances, I could imagine him making a phone call to a friend to go to an ATM and use his card (which may have been left in Georgia or there was a duplicate left there for when he was home or so that his mom could use it to deposit funds. I did the same thing when my child was in college. There were 2 ATM/Debit cards and kept one at home and she had one with her at college.
That's why ALL the Rs cell phone/phone records were so important. Did he call someone? Who? Was there a duplicate card? Were there "middle of the night" phone calls on ANY of their cells or phones? We'll never know, because it wasn't able to be investigated.