Not all of the MacBook Pros had 2nd backlight keyboard cable. So it sounds like either someone replaced the top case with a version that had a two cable backlight keyboard or they swapped out the logic board with an different model.
The fact the backlight ribbon is not plugged in should not effect battery or the sleep sensor in either case. But it does sound like this system may have gotten wet which could be the root issue on why you'er encountering issues here.
So the question is how much did you spend? was it cheap enough given its condition so you can put some money into fixing things the rest of the way? Or should you get your money back and try again?
Try this: Go into your About This Mac and find the systems serial number. Now do the same from the bottom case do they match up? If not plug the last three or four digits into this sites lookup EveryMac and see what it tells you about the cases Vs the systems logic board BIOS claims you have.
Let us know what you discover.
OK, now we have something to work with.
To start with the logic board is expecting a single ribbon cable which could explain why your encountering problems here.
As the signals aren't being connected to the loose backlight ribbon cable and the assignment of the signals within the one ribbon cable maybe why you are having other problems. As the lines signals are expected aren't were they are expected here as well. Luckily, nothing has become damaged here (you may have a blown back light fuse but it doesn't matter right now).
This is a hard question as the cost of getting the correct case pieces and then doing the work to un-frankenstien your system so you have the correct case parts for your i5/i7 system (assuming you want the newer logic bd) may set you back a piece.
I would start looking for the case parts new and also try used (junker) just make sure its not one that got wet. See what it will cost you and then decide. As I don't think you'll fix it any other way here.
You also many have an issue getting this system replaced under the sellers warranty because you have conflicting serial numbers they could claim you switched things around (I know it's a dirty trick). I suspect they got stung here as well when they bought it, or maybe they know, as they did it. So be prepared here on getting a no answer on the return. I will also say the longer you wait the harder it will be to have the courts believe you if you need to go that route.