based on your vid
by watching your video i have a few questions
1. do you have any after market acessories (correct spelling?) hooked up to your car i.e. fog lights
light kit under car. anything that draws power that might not be hooked up or grounded correctly that could drain your battery.
2. have you checked your fuel pump it might not be feeding your engine enough fuel unless you are on the gas?
3. injectors might need to be cleaned. have you replaced them recently were they installed correctly?
4. the altenator could be bad. how old is it wa it replaced recently and if so was it installed correctly? grounded correctly. these are a few ideas that i have.
your cel comes on also. pull the codes and see what they are. it might be some thing simple.
i hope this helps.