Ok. Here is where I am at in my mind as of this moment.
Who actually had motive to kill JonBenet in the family?
Patsy- JonBenet wet the bed constantly. Maybe this could be a reason to snap after a long few exhausting weeks. BUT. Would she really do that considering even Burke admitted they both wet the bed and soiled themselves? Frustrated maybe but not enough IMHO to land a blow to her beauty queen's head and then strangle her. Spank her even.. quite possibly! But I don't think she would intentionally harm her. IMHO this death was intentional. An adult would know that hitting anyone with a heavy object would possibly kill them.
John- She was possibly being molested and John would obviously be on the list of suspects. But why kill her? Just saying IF he HAD been molesting her, why would he kill her? Maybe she threatened to tell is the ONLY reason I could think of. He had, IMHO the least motive.
Burke- Now this is where the motives build up significantly in my humble opinion. Let's start with jealousy. Jealous is a mother of a reason to kill. Burke had all attention on him until JonBenet came along. Then he was (at least in his mind probably) knocked off the "the tit" as us southerners say. He wasn't as important anymore as JonBenet was. (again in his mind possibly). Then add all of the attention his mother gave to JonBenet as the years wore on, and you have a serious storm brewing. Especially if he had any underlying psych issues. Then all of the money and attention the pageants brought to her. The extended family being involved in her costumes and such. Maybe in his mind SHE was getting to do all of these things and mama was watching her gleaming at her future beauty queen. I know that it has been said that Burke was involved in a lot of extra curricular activities, but you have to wonder how MANY were just to keep him busy and no one was fawning over his accomplishments as they did for JonBenet. So basically his activities were only to keep him occupied. Also to make the family look perfect with their kids involved in so many things.
Now, add in other components such as not getting the gifts he wanted (this is kind of something I feel is probably true considering he couldn't even remember the gift he just HAD to sneak down and play with that night) and maybe JonBenet getting everything she wanted. Maybe tensions were quickly rising that morning/ afternoon. By that evening he was totally pi$$ed, especially when he gets home and notices he really didn't get much. MAYBE that's why he snuck down to the basement. To check and see if maybe his parents were hiding a special gift for him for their trip?
Anyway, Burke is eating pineapple and drinking his tea and his little sister who he's possibly seriously despising at this point, come and steals his pineapple. Oh Hell NO. He's had ENOUGH of his bratty spoiled sister. He grabs the flashlight nearby that maybe he used to sneak a peek at the gifts and chases her with it. He's hit her before and got away with it. No telling honestly how many times either. She's thinking she's being chased in fun and jest. Burke however is not in the least bit happy. She runs to the basement where they play, and in the privacy of the basement is when he makes his move. He hits her hard and means it. Maybe he didn't quite realize how fatal it could be but he wanted her to feel his pain some. When she doesn't get up, he just pokes at her with the train track. Maybe she's having seizures or doing something uncontrollably and he doesn't want his mama who may be packing upstairs to hear her. So he finds the cord (used for something entirely different usually) and chokes her from behind. To make her stop doing whatever her body is doing in the last throws of life. He at this point maybe did the strangling out of fear and panic. His mama might have noticed at some point JonBenet wasn't in her bed while she was packing and found her dead. That may have been the scream heard by neighbors. Then the cover-up occurred by the parents. He was sent to his room to stay out of the way. They would deal with him later.
I feel Burke had the most to gain from her death in his eyes at least. This is all my humble opinion, but this is where my mind is at right now. Burke did it in a white hot fit of rage. Something he was prone to probably.