To start with your battery is on its last legs with 770 cycles it also appears not to be charged as well. Until you can charge the battery to at least 80% it will be hard to diagnose if you truly have a sleep issue or not.
You are also expecting Flash based vids (still present on YouTube) to fully stop, they don’t! So if you put your systems lid down and disconnect the MagSafe the battery will run down. And as we can see here with CoconutBattery the battery is very low.
The spring bar you are speaking about sounds like the heatsink. If that is not making good contact that could cause your system to react poorly when running CPU/GPU intensive tasks. Take a clear picture of this part so we can see what it is and what will be needed to fix it.