I can't tell for sure in the video, but it looks like the main hot wire isn't hooked up. It should be a small red wire that hooks to one of the solenoid posts and runs to the key switch. This is what powers everything. If this wire isn't hooked up, the electric start won't work and it also won't fire/spark. It hooks to the same post on the solenoid that the positive battery cable hooks to. I think it's the red wire that's hanging down that's not hooked up.
Most 4-wheeler problems are caused by a loose nut connecting the handlebars and the seat!!
You only need two tools in life -- WD-40 and duct tape. If it doesn't move and should, use the WD-40. If it shouldn't move and does, use the duct tape.