Do-It-Yourself, Repairs and Fixes

I would tend yo disagree a bit with the other comments. First of all, let's talk about the scratch. It does not looks very deep, so most likely no damage to traces. In order to have a short you would also need to have two traces exposed and some metallic object between the two. This also look unlikely to me. I would clean the area with isopropyl alcohol, check it visually. You could also cover up the scratch with nail polish.

Then, the missing capacitor. First of, I cannot make from the picture if there was a capacitor soldered there in the first place. Sometimes there are purposfuly unpopulated components. In any case, all of the capacitors you are seeing on the backside of the CPU are decoupling capacitor. They serve no other purpose than to help stabilize the voltage versus the dynamic power draw. This means that less capacitors equals less stabilisation, but not necessarily incapacity to function. I would clean also clean it up and ensure that no metallic object touches the pads. I would probably not try to replace it, as you have no way of knowing what value the capacitor is supposed to be (usually no schematic/boardview for modern products).

It is theoretically possible to damage the CPU due to a short, but likelihood seems very low to me in this case. I would clean it up, check visually, and try to turn it on.